rheology of low to medium consistency pulp fibre...
TRANSCRIPT
RHEOLOGY OF LOW TO MEDIUM
CONSISTENCY PULP FIBRE
SUSPENSIONS
by
Babak Derakhshandeh
B.A.Sc., Shiraz University, 2004
M.A.Sc., Sharif University of Technology, 2006
A THESIS SUBMITTED IN PARTIAL FULLFILMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
in
The Faculty of Graduate Studies
(Chemical and Biological Engineering)
THE UNIVERSITY OF BRITISH COLUMBIA
(Vancouver)
September 2011
© Babak Derakhshandeh, 2011
ii
Abstract
Papermaking is a major industry to manufacture products vital to education,
communication, and packaging. Most operations in this industry deal with the flow of
different mass concentrations of pulp suspensions. Therefore, the flow properties
(rheology) of pulp suspensions are of great importance for the optimal functionality of
most unit operations in the industry.
Yield stress is one of the most important rheological properties in designing
process equipment, thus needs to be determined by a reliable technique. Two established
and extensively used methods for determining yield stress were compared with a
velocimetry technique. The yield stresses were determined for commercial pulp
suspensions at fibre mass concentrations of 0.5 to 5 wt. %. The results were compared
and models were proposed to predict the yield stress as a function of fibre mass
concentration. The yield stress values obtained by the velocimetry technique were found
to be the most reliable.
Conventional rheometry and local velocimetry techniques were further used to
study the flow behaviour of pulp suspensions beyond the yield stress. Pulp suspensions
were found to be shear-thinning up to a certain high shear rate. The Herschel–Bulkley
constitutive equation was used to fit the local steady-state velocity profiles and to predict
the steady-state flow curves obtained by conventional rheometry. Conventional
rheometry was found to fail at low shear rates due to the presence of wall slip.
Consistency between the various sets of data was found for all suspensions studied.
Finally, the same approach was used to study thixotropy and transient flow
behaviour of concentrated pulp suspension of 6 wt.%. Pulp was found to exhibit a plateau
in the flow curve where a slight increase in the shear stress generated a jump in the
corresponding shear rate, implying the occurrence of shear banding. The velocity profiles
were found to be discontinuous in the vicinity of the yielding radius where a Herschel-
Bulkley model failed to predict the flow. Shear history and the time of rest prior to the
measurement were found to play a significant role on the rheology and the local velocity
profiles of pulp suspension.
iii
Preface
The work of this thesis consists of four different manuscripts, which correspond to
chapters one to four.
Chapter 1 has been published: Derakhshandeh, B., Kerekes, R.J., Hatzikiriakos,
S.G., Bennington, C.P.J, 2011. Rheology of pulp fibre suspensions: A critical review.
Chemical Engineering Science 66(15):3460-3470. I searched, criticised and reviewed the
literature published on the topic. The written work was a collaborative effort between my
supervisors Prof. Chad P.J. Bennington and Prof. Savvas G. Hatzikiriakos, me and Prof.
Richard J. Kerekes.
Chapter 2 has been published: Derakhshandeh, B., Hatzikiriakos, S.G.,
Bennington, C.P.J., 2010. Apparent yield stress of pulp fibre suspensions. Journal of
Rheology 54(5):1137-1154. I performed all the experimental measurements. The written
work was a collaborative effort between my supervisors Prof. Chad P.J. Bennington,
Prof. Savvas G. Hatzikiriakos and me.
Chapter 3 has been published: Derakhshandeh, B., Hatzikiriakos, S.G.,
Bennington, C.P.J., 2010. Rheology of pulp suspensions using ultrasonic Doppler
velocimetry. Rheologica Acta 49 (11-12):1127-1140. I performed all the experimental
measurements. The written work was a collaborative effort between my supervisors Prof.
Chad P.J. Bennington, Prof. Savvas G. Hatzikiriakos and me.
Chapter 4 has been submitted for publication: Derakhshandeh, B., Vlassopoulos,
D., Hatzikiriakos, S.G., 2011. Thixotropy, yielding and ultrasonic Doppler velocimetry in
pulp fibre suspensions. I performed all the experimental measurements. The written work
was a collaborative effort between my supervisor Prof. Savvas G. Hatzikiriakos and me.
Prof. Dimitris Vlassopoulos revised the manuscript and provided insightful advices on
the topic.
Check the first pages of these chapters to see footnotes with similar information.
iv
Table of Contents Abstract .............................................................................................................................. ii
Preface ............................................................................................................................... iii
Table of Contents ............................................................................................................. iv
List of Tables ................................................................................................................... vii
List of Figures ................................................................................................................. viii
Nomenclature ................................................................................................................... xi
Acknowledgments .......................................................................................................... xiv
Dedication ........................................................................................................................ xv
1. Introduction ................................................................................................................... 1
1.1. Literature Review ..................................................................................................... 2
1.1.1. Background .......................................................................................................... 2
1.1.1.1. Fibre Properties and Consistency Ranges ........................................................ 2
1.1.1.2. Fibre Contacts and Forces ................................................................................ 3
1.1.1.3. Forces on Fibres and Flocculation .................................................................... 4
1.1.1.4. Rheology of Fibre Suspensions ........................................................................ 5
1.1.2. Yield stress ........................................................................................................... 5
1.1.2.1. Yield Stress of Fibre Suspensions .................................................................... 7
1.1.2.2. Modified Rheometers ....................................................................................... 8
1.1.2.3. Vaned-Geometry Devices ............................................................................... 10
1.1.2.4. Findings of Various Approaches to Measure Yield Stress ............................. 11
1.1.2.5. Modeling Yield Stress .................................................................................... 13
1.1.3. Shear viscosity .................................................................................................... 14
1.1.3.1. Suspensions of Synthetic Fibres ..................................................................... 14
1.1.3.2. Shear Viscosity of Pulp Suspensions .............................................................. 15
1.1.3.3. Extensional Viscosity of Fibre Suspensions ................................................... 18
1.1.4. Viscoelasticity .................................................................................................... 19
1.1.5. Fluidization of pulp suspensions ........................................................................ 21
1.1.6. Applications in pipe flow ................................................................................... 23
1.1.7. Summary and conclusions .................................................................................. 25
v
1.2. Thesis Objectives ................................................................................................... 26
1.3. Thesis Organization ............................................................................................... 26
2. The Apparent Yield Stress of Pulp Fibre Suspensions ........................................ 29
2.1. Introduction ............................................................................................................ 29
2.2. Velocity Profile Determination Using Ultrasonic Doppler Velocimetry .............. 33
2.3. Materials and Experimental Testing ...................................................................... 36
2.4. Results and Discussion .......................................................................................... 39
2.4.1. Apparent yield stress measurement by linear stress ramps ................................ 39
2.4.2. Apparent yield stress measurement by the start-up of shear flow experiment ... 42
2.4.3. Apparent yield stress measurement by ultrasonic Doppler velocimetry (UDV) 44
2.4.4. Comparison of the different apparent yield stress measurement methods ......... 48
2.5. Summary ................................................................................................................ 53
3. Rheology of Pulp Suspensions Using Ultrasonic Doppler Velocimetry .............. 54
3.1. Introduction ............................................................................................................ 54
3.2. Materials and Experimental Testing ...................................................................... 56
3.3. Results and Discussion .......................................................................................... 56
3.3.1. Conventional rheometry analysis ....................................................................... 56
3.3.2. Velocity profile measurements ........................................................................... 60
3.3.3. Comparison of the conventional rheometry and the UDV techniques ............... 68
3.3.4. Effect of pH and lignin on the rheology of SBK and TMP suspensions ........... 71
3.4. Summary ................................................................................................................ 75
4. Thixotropy, Yielding and Ultrasonic Doppler Velocimetry in Pulp Fibre
Suspensions ...................................................................................................................... 77
4.1. Introduction ............................................................................................................ 77
4.2. Materials and Experimental Testing ...................................................................... 79
4.3. Results and Discussion .......................................................................................... 81
4.3.1. Hysteresis loops .................................................................................................. 81
4.3.2. Transient behaviour during shear flow ............................................................... 84
4.3.2.1. Build-Up Behaviour ............................................................................................. 84
4.3.2.2. Structure Breakdown ........................................................................................... 87
4.3.3. Viscosity bifurcation .......................................................................................... 89
vi
4.3.4. Local velocity profiles ........................................................................................ 91
4.3.5. Rheological interpretation of the velocity profiles ............................................. 95
4.4. Summary ................................................................................................................ 98
5. Conclusions, Contributions to the Knowledge and Recommendations ............ 100
5.1. Conclusions ......................................................................................................... 100
5.2. Contributions to the Knowledge ......................................................................... 102
5.3. Recommendations for Future Work .................................................................... 103
Bibliography .................................................................................................................. 105
Appendix ........................................................................................................................ 124
Appendix A: Ultrasonic Doppler Velocimetry ............................................................... 124
vii
List of Tables
Table 1-1: Apparent yield stress of SBK suspension obtained using different methods . 13
Table 2-1: Properties of pulp fibres used in the present study ......................................... 37
Table 2-2: Optimum pre-shearing conditions applied on pulp suspensions .................... 38
Table 2-3: Apparent yield stress by the linear shear stress ramp method ........................ 40
Table 2-4: Apparent yield stress by start-up of steady shear flow experiment ................ 43
Table 2-5: Apparent yield stress by UDV coupled with a rate-controlled viscometer .... 47
Table 2-6: Summary of fitted constants to the power-law model .................................... 52
Table 3-1: Critical shear stress for the onset of turbulence in pulp suspensions ............. 59
Table 3-2: Herschel–Bulkley constants for pulp suspensions ......................................... 67
Table 3-3: Percentage increase of the apparent yield stress and consistency index of SBK
and TMP pulp suspensions compared with those at pH=4 ........................... 74
Table 4-1: Thixotropic time constants for build-up ......................................................... 87
Table 4-2: Thixotropic time constants for breakdown ..................................................... 89
viii
List of Figures
Figure 1-1: Instantaneous viscosity vs shear stress by linear shear stress ramp ................ 6
Figure 1-2: Apparent stress to initiate flow ....................................................................... 7
Figure 1-3: Ultimate shear strength ................................................................................... 8
Figure 1-4: Storage modulus and loss modulus as a function of strain. ........................... 9
Figure 1-5: Vane in baffled housing used to study pulp fibre suspensions ..................... 10
Figure 1-6: Shear stress versus shear rate for 0.05% mixed pulp fibre suspensions ....... 17
Figure 1-7: Friction loss curve for chemical pulp ............................................................ 24
Figure 2-1: Ultrasonic Doppler velocimetry in Couette geometry .................................. 34
Figure 2-2: Schematic of vane in large cup with yielded and un-yielded regions ........... 36
Figure 2-3: Repeats of apparent yield stress measurements for SBK .............................. 39
Figure 2-4: Creep response of a bleached softwood kraft pulp suspension ..................... 40
Figure 2-5: The apparent yield stress of pulp suspensions as a function of mass
concentration by using the shear shear stress ramps ................................... 41
Figure 2-6: Stress response after imposition of steady shear at vane rotational rate of 8
rpm ............................................................................................................... 42
Figure 2-7: The apparent yield stress of pulp suspensions as a function of mass
concentration by applying the start-up of steady shear flow ....................... 43
Figure 2-8: Velocity profiles across the gap .................................................................... 46
Figure 2-9: The apparent yield stress of pulp suspensions as a function of mass
concentration using local velocity profile measurements ............................ 47
Figure 2-10: Comparison of the apparent yield stress obtained using three different
methods ........................................................................................................ 50
Figure 3-1: Steady-state flow curves of several 2.5 wt.% pulp suspensions at 23°C ...... 57
ix
Figure 3-2: The critical shear stress for the onset of turbulence or fluidization of several
pulp suspensions as a function of fibre mass concentration.. ...................... 59
Figure 3-3: Velocity profiles across the gap for 3 wt.% pulp suspensions at 23°C and
rotational speeds of 2, 8 and 16 rpm. ........................................................... 62
Figure 3-4: Velocity profiles across the gap for pulp suspensions at 23°C, vane rotational
rate of 16 rpm and several mass concentrations.. ........................................ 65
Figure 3-5: Steady-state flow curves for pulp suspensions at 23°C and several mass
concentrations.. ............................................................................................ 70
Figure 3-6: Velocity profiles across the gap for SBK at vane rotational rate of 16 rpm at
23°C and pH=4,6, 8 and 10 .......................................................................... 72
Figure 3-7: Velocity profiles across the gap for TMP at vane rotational rate of 16 rpm at
23°C and pH=6, 8 and 10. ............................................................................ 74
Figure 4-1: Hysteresis loop for 6 wt.% pulp fibre suspension ......................................... 81
Figure 4-2: Apparent flow curves of pulp fibre suspension. .......................................... 83
Figure 4-3: Structure build-up in pulp suspensions ......................................................... 85
Figure 4-4: Structure breakdown in pulp suspensions. .................................................... 88
Figure 4-5: Creep tests and viscosity bifurcation ............................................................ 90
Figure 4-6: Steady-state velocity profile of pulp at a vane rotational rate of 16 rpm. Pulp
was pre-sheared at 350 Pa for 2 minutes with no time of rest after............. 92
Figure 4-7: Steady-state velocity profiles of pulp suspension at a vane rotational rate of
16 rpm. Pulp was pre-sheared at 350 Pa for 2 minutes and left at rest for 0,
60 and 120 minutes prior to the velocity measurement ............................... 93
Figure 4-8: The yielding radius as a function of the rest time deduced from the steady-
state velocity profiles ................................................................................... 94
Figure 4-9: Transient velocity profiles of pulp suspension when the vane rotational rate
was suddenly increased to 16 rpm. Pulp was pre-sheared at 350 Pa for 2
minutes and left at rest for 5 minutes prior to the velocity measurement .... 95
x
Figure 4-10: Steady-state velocity profiles at rotational rates of 8, 16 and 32 rpm ......... 96
Figure 4-11: Master curve obtained from steady-state velocity profiles ......................... 98
Figure A-1: Ultrasound velocimeter coupled with a rate controlled rheometer ............ 125
xi
Nomenclature
A fibre aspect ratio, (-)
a constant, (Pa)
b constant, (-)
c sound velocity in the medium, (m/s)
Cm fibre mass concentration, (%)
Cv fibre volume concentration, (%)
Cs sediment concentration, (%)
d inner diameter of fibre, (mm)
D outer diameter of fibre, (mm)
Dr particle rotary diffusion, (s-1
)
DT outer housing diameter, (m)
DR rotor diameter, (m)
E fibre's modulus of elasticity, (Pa)
fd frequency shift of the reflected ultrasound pulses, (Hz)
f0 ultrasound emission frequency, (Hz)
G′ storage modulus, (Pa)
G″ loss modulus, (Pa)
h vane height, (mm)
K HB consistency index
kB Boltztmann constant, (m2Kg s
-2 K
-1)
L fibre length, (mm)
m constant
n HB power-law index
N crowding number, (-)
NG gel crowding number, (-)
r local radius within the gap of the rheometer, (mm)
R dimensionless radius
R1 vane radius, (mm)
xii
R2 cup radius, (mm)
Ry yielding radius, (mm)
t time, (s)
tf time delay of the reflected ultrasound pulses, (s)
T torque, (N.m)
T absolute temperature, (K)
)(ru local velocity across the gap of the rheometer, (mm/s)
u(y) velocity in the direction of acoustic axis, (mm/s)
U scaled velocity, (s-1
)
V pipe flow velocity, (m/s)
VL lumen volume per unit mass of fibre (m3/kg fibre)
Xw water mass located in the fibre wall, (kg water/kg fibre)
y distance of fibres from the outer wall in Couette geometry, (mm)
∆H pipe friction loss, (Pa)
Greek letters
Α constant
Β constant
Γ strain, (%)
.
γ shear rate, (s-1
)
φg volume fraction of gas phase in suspension, (-)
η Instantaneous viscosity, (Pa.s)
ηs medium viscosity, (Pa.s)
η0 suspension viscosity prior to shearing, (Pa.s)
η∞ suspension viscosity after shearing, (Pa.s)
µa apparent viscosity, (Pa.s)
bρ bulk density, (kg/m3)
fρ fibre density, (kg/m3)
wρ water density, (kg/m3)
xiii
σ shear stress, (Pa)
σi pre-shear stress, (Pa)
σe final shear stress in the step-wise experiments, (Pa)
σc critical shear stress, (Pa)
σy apparent yield stress, (Pa)
σT steady-state shear stress at the vane, (Pa)
εf power dissipation/unit volume, (w/m3)
ω fibre coarseness, (g/m)
θ emission angle into the fluid
τ structure build-up/breakdown time constant, s
Abbreviations
SBK bleached softwood kraft pulp suspension
TMP thermal mechanical pulp suspension
SGW stone ground wood pulp suspension
HW hardwood pulp suspension
UDV ultrasound Doppler velocimetry
xiv
Acknowledgments
I offer my sincere gratitude and appreciation to my thesis supervisors Prof. Chad
P.J. Bennington and Prof. Savvas G. Hatzikiriakos for giving me insightful scientific
advice. They have supported me throughout my thesis with their patience and knowledge
whist allowing me the room to work in my own way. One simply could not wish for
better or friendlier supervisors.
My utmost gratitude to Prof. Chad P.J. Bennington who passed away
unexpectedly on February 14, 2010 for introducing me into pulp and paper science and
technology, for his smile, sincerity and encouragement. He will be in my thoughts and in
my prayers for ever.
Working in the Dynamic Mixing and Rheology Group has been a privilege. I
would love to thank all members, both past and present, for their hard work that has
inspired so many ideas. I would like to thank my friends and ex-colleagues Dr. Christos
Stamboulides and Dr. Anne-Marie Kietzig for their unconditional support.
I am grateful for the financial support of the University of British Columbia 4YF
and DuPont fellowship in pulp and paper.
From the bottom of my heart, I thank my good friends Hooman Rezaei and
Fahimeh Yazdanpanah, and my brother Maziar Derakhshandeh for helping me get
through the difficult times, and for all the emotional support, camaraderie, entertainment,
and caring they provided.
The most profound and loving thanks to my family, to my parents who have given
me the greatest love and support anyone could ever expect. I am blessed to have them and
I have missed them deeply during these years. They are my true inspiration.
xv
Dedication
This thesis is dedicated to my parents, my sister and brother, for always
encouraging and supporting me to achieve my goals.
1
1. Introduction1
Flow of fibre suspensions is a key factor in manufacturing a diverse range of
products, for example, fibre-reinforced composites, food stuffs, carpeting, and textiles
(Tucker and Advani, 1994; Papathanasiou and Guell, 1997; Piteira et al., 2006; Umer et
al., 2007). Of these industries, none is larger than pulp and paper manufacture. It is a
major industry in almost all countries, producing communication papers, packaging,
boxes, tissue, hygiene products, and an assortment of disposable products. Fibre for this
industry comes from pulping biomass, mostly trees in modern times. As such, the
industry is based on a sustainable, renewable, carbon-neutral resource.
There is growing interest in new uses of biomass. The world’s increasing
population requires that more energy and products come from renewable resources that
do not impinge upon the food supply. The forest biomass is a logical source. As in the
case of pulp and paper, processing biomass for these new applications will require
handling of fibres in suspension.
This work focuses on the rheological characterization of pulp fibre suspensions.
Conventional stress-controlled and rate-controlled rheometers along with ultrasonic
Doppler velocimetry are used to characterize commercial pulp fibre suspensions of
various fibre mass concentrations. Particular objectives are to measure apparent yield
stress, to study post-yield flow behaviour, and to investigate thixotropy and time
dependent flow behaviour of pulp fibre suspensions. Constitutive models are proposed to
describe the flow behaviour of pulp suspensions over a wide range of shear rates and
fibre mass concentrations.
1 A version of this chapter has been published. Derakhshandeh, B., Kerekes, R.J., Hatzikiriakos, S.G.,
Bennington, C.P.J., 2011. Rheology of pulp fibre suspensions-A critical review. Chemical Engineering
Science 66(15): 3460-3470.
2
1.1. Literature Review
1.1.1. Background
1.1.1.1. Fibre Properties and Consistency Ranges
Wood pulp fibres are hollow tubes having typical average length 1-3 mm and
diameter 15-30 µm. There is a wide variability around these averages, even within one
species. Accordingly, fibre length is specified by various weighted averages, a typical one
being length-weighted average for fibre length to give weight to the longer fibres in the
distribution.
Wood fibres are composites made up of spirally-wound fibrils of cellulose. Some
newer applications of wood pulp are being developed to exploit the unique properties of
these fibrils. Examples are micro-fibrillated cellulose (MFC) and nano-crystalline
cellulose (NCC). MFC are small fibrous particles of length 100 to 1000 nm and diameter
5-30 nm (Ankerfors and Lindström, 2010). NCC is smaller, in the range 20-200 nm in
length (Dong et al., 1998; Pan et al., 2010). These fibrous particles are in the Brownian
range and generally behave as colloidal suspensions in the dilute range and as gels when
more concentrated. They are outside the range of interest in this study, although in
producing them, for example in homogenizers, grinders, refiners and like, rheology of
pulp suspensions plays a role.
Suspensions of pulp fibres are processed in various ranges by mass consistency,
Cm (mass of fibres divided by the total mass of suspension). Kerekes et al. (1985)
classified the ranges as follows: low consistency (Cm=0-5%) where the suspension is
water-fibre slurry; medium consistency (Cm=5-20%) formed by mechanically pressing
water from a medium consistency suspension and ultra-high consistency (Cm>40%)
formed by evaporative drying.
At low consistency, the suspension is a two-phase slurry, changing at medium and
higher consistencies into a three phase heterogeneous mixture of water, fibres and air. At
the higher gas contents, it is useful to use volumetric concentration, Cv, in place of mass
consistency. These are related as follows:
3
bL
w
w
f
mv VX
CC ρρρ
++=
1 (1-1)
where Cm is the fibre mass fraction, fρ is the fibre density (kg/m3), wρ is the water
density (kg/m3), bρ is the bulk density (kg/m
3), Xw is the water adsorbed within the fibre
wall (kg water/kg fibre) and VL is the volume per unit mass of the hollow channel in the
middle of the fibre referred to as lumen (m3/kg fibre).
All of the above consistency ranges are found in the processes for pulp and paper
manufacture. They are likely to be important in new processes for fibrous biomass.
1.1.1.2. Fibre Contacts and Forces
The large aspect ratio of pulp fibres (40 to 100) induces significant contact among
fibres at all consistencies. This has a strong effect on suspension rheology. In the low
consistency range, with increasing consistency the nature of contacts changes from
occasional collisions, to forced contacts, to continuous contact. These contact regimes
have been described by a crowding number, N, defined as the number of fibres in a
volume swept out by the length of a single fibre (Kerekes et al., 1985). This parameter
can be expressed in terms of a volumetric concentration Cv, fibre length L, and diameter
d. Pulp fibres have a distribution of fibre lengths, variable diameters, and like all
lignocelluloses materials, tend to swell in water. Accordingly mass is more suitable than
volume for calculating numbers of fibres and thereby N. Kerekes and Schell (1992)
provide a mass-based expression for this calculation shown below:
ω
22
53
2 LC
d
LCN mv ≈
= (1-2)
In this equation, L is the length-weighted average length of the pulp fibres (m); Cm
is the mass consistency (%), and ω is the fibre coarseness (weight per unit length of
fibre, kg/m). The latter is a commonly measured property of pulp fibres. Accordingly, the
constant has units kg/m3.
4
In early work, Mason (1950) identified 1=N as a “critical concentration” at
which, collisions first occur among fibres in shear flow. In later work, Soszynski and
Kerekes (1988a) and Kerekes and Schell (1992) showed that at 60N ≈ fibre suspensions
have about three contacts per fibre. This is a critical value because fibres are restrained by
three-point contact. Upon cessation of shear, fibres become locked in the network in a
bent configuration. This elastic bending creates normal forces at contacts, and the
resulting frictional force imparts mechanical strength to the network.
In later work, Martinez et al. (2001) identified another critical value of N, 16N ≈ ,
calling this a “gel crowding number”. Below this value, the suspension behaves as
essentially dilute. In recent work, the limits N=16 and N=60 were shown to correspond
respectively to the “connectivity threshold” and “rigidity threshold” of fibre networks as
predicted by effective-medium and percolation theories (Celzard et al., 2009).
1.1.1.3. Forces on Fibres and Flocculation
In addition to friction forces, other forces may contribute to strength at contacts,
such as forces from chemical flocculants, hooking of curved fibres, and surface tension
when air content is substantial (Kerekes et al., 1985). These forces impart mechanical
strength to fibre networks.
In shear flow, fibres aggregate into local mass concentrations called flocs, which
are typically a few fibre lengths in size. When N<60, the flocs are loose aggregates, but
when N>60 the flocs adopt mechanical strength. Their size and strength are affected by
the flow conditions, for example, shear history such as nature of the decaying turbulence
in the wakes of pumps and mixers where most flocs form (Kerekes, 1983b). Having a
larger concentration than the suspension average, flocs also have a larger strength than
the suspension average. Consequently, fibre suspensions are heterogeneous in both mass
and strength, an important factor in pulp suspension rheology.
The mechanism of floc formation has been studied in various past works. Kerekes
(1983b) examined the role of decaying turbulence in floc formation, and later Soszynski
and Kerekes (1988b) studied the role of flow acceleration and turning on local fibre
5
crowding to produce coherent flocs. Valuable insights have also been gained from
particle level simulation techniques modeling fibres as chains of rigid rods connected
with hinges (Ross and Klingenberg, 1998; Schmid and Klingenberg, 2000a,b,c).
In summary, fibre suspensions display a large range of behaviour, from dilute
slurries, to heterogeneous two-phase suspensions, to discontinuous three-phase mixtures
of wet fibres in a gas. In commercial papermaking, pulp suspensions are formed into
paper by filtration in the range 16 60N< < to minimize both water usage and
flocculation. However, most of the unit operations for processing pulp before
papermaking take place at one or other of the higher consistency ranges.
1.1.1.4. Rheology of Fibre Suspensions
The complexities described above make the rheology of pulp suspensions
complex. The suspension often cannot be treated as a continuum because fibres and flocs
are large relative to the dimensions of the flow field. Both shear history and time in a
given shear flow (thixotropy) may cause floc size and strength to differ among
suspensions even when suspension averages are the same. Fibre orientation and migration
away from solid boundaries create a depletion layer near walls which complicates
rheological measurements (Nguyen and Boger, 1992; Barnes, 1997; Swerin, 1998;
Wikström and Rasmuson, 1998). Given these factors and those described earlier, not
surprisingly defining and measuring rheological properties of fibre suspensions is
complex. The complexities involved in the rheological measurement of pulp fibre
suspensions will be discussed in more detail throughout the next chapters of this thesis.
1.1.2. Yield stress
Yield stress is arguably the most important rheological property of fibre
suspensions. Unless it is exceeded, flow does not take place. As a rheological property,
yield stress has various definitions and means of measurement. These will be discussed in
detail in chapter 2 of this thesis although a brief overview of the yield stress measurement
techniques, definitions, and findings of past work is summarized here.
6
In the simple case of a Bingham fluid, yield stress is the shear stress required to
initiate continuous motion in the form of Newtonian flow. However, non-Newtonian
fluids often exhibit no clear demarcation as found in a Bingham fluid. Indeed there is
some controversy over whether yield stress is a true material property (Scott, 1933;
Barnes and Walters, 1985). Accordingly, it is common to define an “apparent yield
stress” by the method of measurement. There are several approaches for doing so that are
relevant to fibre suspensions:
“Maximum viscosity”: This yield stress is the value of shear stress at which the
instantaneous viscosity exhibits a significant decrease as shear stress is increased, as
shown in Figure 1-1 (Cheng, 1986; Zhu et al., 2001; Brummer, 2005; Coussot, 2005;
Nguyen et al., 2006).
Figure 1-1: Instantaneous viscosity versus shear stress by applying a linear shear stress
ramp. Apparent yield stress is defined as the shear stress at which, the instantaneous
viscosity starts dropping.
“Apparent stress to initiate flow”: This apparent yield stress is the intercept obtained by
extrapolating shear stress to zero shear rate, usually from the linear portion of the shear
stress-shear rate curve (Figure 1-2).
7
Figure 1-2: Apparent stress to initiate flow
“Ultimate Shear Strength”: This yield stress is the maximum stress reached as strain is
increased to initiate flow, after which the stress decreases. The maximum is called the
ultimate shear strength (Figure 1-3), and used as a measure of the apparent yield stress
(Thalen and Wahren, 1964; Nguyen and Boger, 1985; Cheng, 1986; Liddell and Boger,
1996). The rationale here is that this stress must be exceeded for flow to take place.
1.1.2.1. Yield Stress of Fibre Suspensions
There have been two general approaches to measuring yield stress of pulp fibre
suspensions (Kerekes et al., 1985). The first, a “quasi-static” shear strength, employs
conventional stress-controlled or rate-controlled rheometers or devices that rupture the
fibre network at rest. The second, a “dynamic network strength”, is obtained in flowing
suspensions by estimating the shear stress at the surface of plugs of fibre networks at the
onset of plug surface disintegration. This gives a “disruptive shear stress” (Daily and
8
Bugliarello, 1961; Meyer and Wahren, 1964; Mih and Parker, 1967; Duffy and Titchener,
1975; Bennington et al., 1990).
Figure 1-3: Ultimate shear strength
1.1.2.2. Modified Rheometers
Narrow-gap, smooth-walled rheometers must be modified to measure pulp
suspensions for reasons described earlier. To accommodate the size of fibres and flocs,
the gap size is increased. To overcome the depletion layer, rheometer walls may be
roughened with asperities that are large relative to the thickness of the depletion layer.
Swerin et al. (1992) and Damani et al. (1993) measured the apparent yield stress of pulp
suspensions in a parallel-plate rheometer having roughened walls of 105-125 µm and a
gap size of 10 mm.
9
Oscillatory shear is another approach to measure the apparent yield stress. The
suspension is subjected to an oscillatory small-amplitude strain to measure material
properties such as elastic and viscous modulus (Dealy and Wissbrun, 1990). Swerin et al.
(1992) and Damani et al. (1993) used oscillatory rheometry to measure the apparent yield
stress of softwood pulp suspensions from the product of the storage modulus G′ and the
critical strain for the onset of decrease of G′ in oscillatory shear modes (Figure 1-4). In
this measurement small strains are applied which may cause strain and rupture only
between flocs, not within them. Swerin et al. (1992) found the critical strain to be almost
independent of the mass concentration, which suggests that the strain was confined to
zones between flocs.
Figure 1-4: Storage modulus () and loss modulus () as a function of strain. The critical
shear strain (γc) defines the limit of linear viscoelasticity and is used to obtain the
apparent yield stress of pulp suspensions (Swerin et al., 1992).
10
1.1.2.3. Vaned-Geometry Devices
Another approach to overcome issues of gap size and wall slip to measure the
apparent yield stress is by use of vaned rotors in housings having baffles, as shown in
Figure 1-5 (Head, 1952; Duffy and Titchener, 1975; Gullichsen and Harkonen, 1981;
Bennington et al., 1990). This approach moves the shear layer away from the wall surface
to a circle swept out by the tips of the rotor vanes, that is, into the body of the suspension.
The shear plane lies in the circle swept out by the rotor tips.
Head (1952), Thalen and Wahren (1964 a,b), Duffy and Titchener (1975),
Gullichsen and Harkonen (1981), Bennington et al. (1990), Ein-Mozaffari et al. (2005)
and Dalpke and Kerekes (2005) employed vaned-geometry devices to measure the
apparent yield stress of pulp suspensions. They applied increasing strain on the rotor and
reported the apparent yield stress as the maximum stress sustained by the suspension at
the onset of continuous motion. This corresponds to the “ultimate shear strength”
discussed earlier. Most of the studies were for low and medium consistency pulp
suspensions, but Bennington et al. (1995) extended measurement of apparent yield stress
to high consistency which contained significant amounts of air.
Figure 1-5: Vane in baffled housing used to study pulp fibre suspensions (Head, 1952).
11
1.1.2.4. Findings of Various Approaches to Measure Yield Stress
All workers found the apparent yield stress to depend on a power of the
consistency. At low consistency, the power dependence is for the difference between the
consistency being tested and a threshold consistency at which networks form. The
premise here is that consistencies below the threshold do not contribute to mechanical
strength. Thalen and Wahren (1964a) defined the threshold by a sediment concentration,
Cs, as shown in Eq. (1-3) below. Later, Martinez et al. (2001) defined it by the gel
crowding number NG as shown in Eq. (1-4).
( )b
smy CCa −=σ (1-3)
or
( )b
Gy NNa −=σ where 16G
N = (1-4)
These equations apply for low consistency pulp suspensions, typically in the
range in which paper is formed, typically Cm=0.5 to 1%. However, most processing of
fibre suspensions takes place at larger consistencies, typically are 3% or more. In this
range, the apparent yield stress equations can be simplified to:
b
my aC=σ (1-5)
where m
C is consistency in % and a has units of Pa.
Values for a and b measured in earlier studies were summarized by Kerekes et al.
(1985). The studies examined apparent yield strength in various ways, including shear
strength of pulp plug surfaces in flowing suspensions, and defined these strengths in
differing ways. In addition, many other factors differed among the studies, such as wood
species and pulping method. Not surprisingly, results varied considerably. Values of a
were in the range 1.8 <a< 24.5 (Pa) and b in the range 1.69<b<3.02. Many key variables
contributing to these differences were not measured or reported. For example, Dalpke and
Kerekes (2005) found fibre length to be very important, with longer fibres causing larger
apparent yield stress.
12
At consistencies Cm>8%, fibre suspensions generally contain substantial air.
Bennington et al. (1995) measured the apparent yield stress in ranges of consistency
having up to 90% air content by volume, obtaining the following expression for yield
stress:
( ) 6.04.32.35 1107.7 AC gmy ϕσ −×= (1-6)
5.0004.0 ≤≤ mC and 9.00 ≤≤ gϕ
where g
ϕ is the fractional gas content and A is the fibre axis ratio with the pre-factor
numerical constant in Pa. This equation is valid for both mechanical and chemical pulps.
At high gas contents, it was found that the apparent yield stress could be well described
by volumetric fibre concentrationv
C (Bennington et al, 1990):
b
y vaCσ = (1-7)
All the measurements of apparent yield stress have considerable scatter, often as
much as 100%. To determine an average value, Bennington et al. (1990) defined a
relative apparent yield stress to be that measured in a single test divided by the average
apparent yield stress for all tests performed under the same experimental conditions.
Using the relative apparent yield stress, experimental data were compared on a
normalized basis and approximated by a Gaussian distribution. The coefficient of
variation for the apparent yield stress of pulp suspensions was found to be 20% and for
synthetic fibres to be 45%.
Scatter in the data is due to many factors, including how apparent yield stress is
defined and the method of measurement. For example, apparent yield stresses obtained
by quasi-static methods were all larger than those measured using dynamic methods.
Other difference are illustrated in the methods and definitions employed in studies of
Gullichsen and Harkonen (1981), Bennington et al. (1990), Swerin et al. (1992),
Wikström et al. (1998), and Dalpke and Kerekes (2005). An example is given in Table 1-
1 for apparent yield stress of a bleached softwood kraft pulp. The values range from 19.3
to 350 Pa for a consistency of 3%, and from 60 to 1220 Pa for a consistency of 6%.
13
Table 1-1: Apparent yield stress of SBK suspension obtained using different methods
Reference Measurement method σy (Pa)
Cm=3%
σy (Pa)
Cm=6%
Bennington et al. (1990) Baffled concentric-cylinder,
Ultimate shear strength 176 1220
Swerin et al. (1993) Couette cell, Oscillatory
experiments 19.3 117
Damani et al. (1993) Parallel plate geometry,
Oscillatory experiments ------ 60
Wikström et al. (1998) Baffled concentric-cylinder,
Ultimate shear strength 131 1100
Ein-Mozaffari et al. (2005) Concentric-cylinder, Ultimate
shear strength 350 ------
Dalpke and Kerekes (2005) Vane in large cup geometry,
Ultimate shear strength 130 ------
1.1.2.5. Modeling Yield Stress
Several workers developed mathematical models of fibre networks to predict
yield stress. Bennington et al. (1990) derived an equation based on network theory that
included fibre aspect ratio and Young’s modulus as follows:
32
vy CcEA=σ (1-8)
where A is the fibre aspect ratio, E is the fibre’s Young’s modulus, c is a constant and Cv
is the volume concentration of the pulp suspension. All fibres were assumed to be rod-
like with a common area moment of inertia. In later work, Wikström et al. (1998)
considered differing area moments of inertia for pulp fibres and modified Eq. (1-8) by
using the fibre stiffness (the product of elastic modulus and area moment of inertia). This
modification led to the following equation proposed for the apparent yield stress values:
3
4
42 1 vy C
D
dcEA
−=σ (1-9)
where d and D are the inner and outer diameters of the fibres.
14
1.1.3. Shear viscosity
1.1.3.1. Suspensions of Synthetic Fibres
Relatively few studies have been devoted to measuring the viscosity of pulp
suspensions, although there have been a substantial number for the simpler case of
synthetic (plastic, glass) fibres of uniform size and shape. Although this study is focused
on pulp fibres, there are sufficient similarities to synthetic fibres to warrant a brief
discussion here.
References to many of the major studies of synthetic fibres can be found in review
papers and literature surveys in papers on the subject, for example Ganani and Powell
(1985), Bennington and Kerekes (1996), Petrie (1999), Kerekes (2006), and Eberle et al.
(2008). Some studies are particularly relevant to pulp fibre suspensions. Nawab and
Mason (1958) measured the viscosity of dilute suspensions of thread-like rayon fibres in
castor oil. They employed a bob and cup viscometer equipped with a microscope to check
for wall slippage. Fibre aspect ratio had a strong effect on suspension viscosity and its
shear dependence. In other work, Blakeney (1966) examined the effect of fibre
concentration on the relative viscosity of suspensions of straight, rigid nylon fibres with
aspect ratio of about 20. He found that at Cv>0.0042, viscosity increased dramatically
with concentration. Interestingly, this condition is 1≈N .
Ziegel (1970) measured the viscosity of suspensions of glass rods, glass plates and
asbestos fibres in high viscosity polymer fluids and compared them with those of
spherical particles. Horie and Pinder (1979) measured the viscosity of suspension of
nylon fibres over a wide range of consistency and shear rates; they found thixotropy and
that thickness of the shearing layer in the viscometer to depend on time of shearing.
Kitano and Kataoka (1981) employed a cone-plate rheometer to study the steady
shear flow properties of suspensions of vinylon fibres in silicone oil up to Cm=7%.
Ganani and Powell (1986) studied the rheological behaviour of monodisperse glass fibres
both in Newtonian and non-Newtonian suspending media at fibre volume fractions of
0.02, 0.05 and 0.08. Milliken et al. (1989) employed falling-ball rheometry to measure
viscosity of monodisperse randomly oriented rods in a Newtonian fluid. Suspensions
15
exhibited Newtonian behaviour at Cv< 0.125 and a sharp transition at Cv > 0.125 at which
viscosity depended on the third power of concentration. This corresponds to N=33.
Petrich et al. (2000) studied the relationship between the fibre orientation
distribution, fibre aspect ratio, and the rheology of fibre suspensions. They measured both
specific viscosity and normal stress differences. Chaouche and Koch (2001) examined the
effect of shear stress and fibre concentration on the shear-thinning behaviour of rigid
fibre suspensions. They showed that fibre bending and a non-Newtonian suspending
liquid played a major role in shear-thinning behaviour of suspension at high shear rates.
Switzer and Klingenberg (2003) modelled the viscosity of fibre suspensions. They
showed viscosity to be strongly influenced by fibre equilibrium shape, inter-fibre friction,
and fibre stiffness.
1.1.3.2. Shear Viscosity of Pulp Suspensions
Steenberg and Johansson (1958) studied flow behaviour of suspensions of
unbleached sulphite pulp in a custom-made parallel-plate viscometer. They measured
shear stress-shear rate relationships over a wide range of flow velocity and consistencies
up to 2.5%. They observed two transition points: a maximum at low shear rates and a
minimum at high shear rates. These correspond to similar observations in pipe flow
(discussed later). The transition points shifted towards higher shear rates as the gap
clearance decreased. They measured viscosities at shear rates above the second transition
point where pulp was considered to be a fully sheared medium. At these high shear rates,
they found Newtonian behaviour up to about 100N ≈ , with viscosity slightly larger than
water. This work showed that various flow regimes may exist in rheometers.
In another early study, Guthrie (1959) measured the apparent viscosities of pulp
suspensions at Cm<2% to calculate Reynolds numbers in a pipe. He found viscosity
increased dramatically with consistency above a critical value of Cm=1.4%. Below this,
pulp suspension viscosity showed no significant dependence on the fibre length over the
length range of 0.2-0.67 mm. The likely explanation for this observation is that
consistency 1.4% at fibre length 0.67 mm give about 20N = , which is near the gel
crowding number. Below this the suspension behaves as dilute and length would not be
16
expected to be important. An abrupt change in suspension behaviour at this point is to be
expected.
Chase et al. (1989) surveyed the variation of torque versus rotational rate of
hardwood and softwood pulp suspensions to study the effects of fibre concentration and
freeness on the viscosity parameter. For both suspensions, viscosities increased linearly
with consistency. The viscosity of hardwoods decreased linearly with freeness, while the
viscosity of softwoods increased initially and then decreased with a decrease in freeness.
They also concluded that pulp behaves as a Bingham plastic fluid on the basis that
exhibits an apparent yield stress.
Chen et al. (2003) studied the flow behaviour of pulp suspensions in a modified
parallel-plate rheometer. The lower plate was replaced with a Petri dish to prevent the
suspension overflow, but no modification was made to minimize wall slippage. Softwood
and hardwood bleached kraft pulps were mixed in different ratios, but the total mass
concentration was kept at 0.05%, giving a very dilute suspension i.e. 5N ≈ . They
measured shear stress as a function of shear rate and performed stress relaxation
experiments. Using a CCD camera, they identified three flow regimes as illustrated in
Figure 1-6. In the first regime, Newtonian flow was observed at low shear rates. In the
second regime, they observed unstable flow, with jumps in the shear stress dependent on
shear rate. The stress jumps were attributed to the flocculation of pulp fibre suspensions.
The third region was found to be a dynamic equilibrium zone which showed Newtonian
behaviour at high shear rates.
These studies clearly show that differing flow regimes may exist in rheometers
caused by differences in fibre orientation, a depletion layer, and the onset of shear over
the entire gap as opposed to a depletion layer near the wall. No consistent picture has
been established of when these regimes exist.
17
Figure 1-6: Shear stress versus shear rate for 0.05% mixed pulp fibre suspensions. Three
different regimes were observed for pulp suspensions (Chen et al., 2003).
To avoid wall effects and ensure flow throughout the vessel, Bennington and
Kerekes (1996) measured viscosity by an indirect approach. They created turbulence in a
large-gap device and obtained viscosity from the relationship between power dissipation
and microscale turbulence. They noted, but did not measure, the dependence of viscosity
on shear rate. They found viscosities to depend upon the third power of consistency for
fibre mass consistencies over 1% as shown below:
1.33105.1 mC−×=η (1-10)
where Cm is mass consistency and η is in Pas. Interestingly, the consistency dependence
of the pulp viscosity is similar to that of suspensions of rod-like particles in Newtonian
fluids (Miliken et al., 1989; Powell et al., 2001).
Another approach to characterizing the viscosity of a pulp suspension is by
considering flocs rather than fibres as the suspended solid, specifically flocs to be solid
18
spheres. This is possible in some cases of low velocity flows. Van de Ven (2006) used
this approach to correlate spouting velocity to fibres mass in spouted beds.
Other recent work has addressed the question of viscosity of pulp suspensions in
narrow channels much smaller than a fibre length. In this case, continuum conditions
clearly do not exist and therefore the suspension cannot be considered a fluid.
Consequently, a meaningful viscosity cannot be measured. For practical applications in
process equipment, Roux et al. (2001) introduced the concept of a “shear factor”, a
parameter to be multiplied by velocity divided by a gap size.
1.1.3.3. Extensional Viscosity of Fibre Suspensions
Extensional (elongational) viscosity is the resistance of a fluid element to
stretching in flow. There are few studies of extensional viscosity of pulp fibre
suspensions although there have been some for synthetic fibres. Mewis and Metzner
(1974) measured apparent extensional viscosity of glass fibre suspensions in the range
N>60. They found the extensional viscosity to be one to two orders of magnitude greater
than that of the suspending fluid. Ooi and Sridhar (2004) employed filament stretching
technique to study extensional flow of fibre suspensions in Newtonian and non-
Newtonian fluids.
Studies on extensional flow of pulp fibre suspensions have largely been confined
to measuring stretching and rupture of individual flocs. This work was stimulated by
early findings of Kao and Mason (1975) which showed that flocs ruptured primarily in
tension rather than shear, suggesting that extensional flows were likely to be more
effective than shear flow in dispersing flocs in papermaking.
Kerekes (1983a) employed a high speed camera to study the behaviour of 0.5%
long-fibred pulp suspensions in entry flow into constrictions. These strong flocs were
found to stretch by a ratio up to 5:1 before rupture. The necessary degree of contraction in
the sharp-edge constriction to create this elongational strain was such that flocs came into
contact with constriction edges, which introduced shear on the floc. In other work, Li et
al. (1995a) examined pulp suspensions in extensional flows by nuclear magnetic
resonance imaging technique. They measured the axial velocity profiles for hardwood
19
kraft pulps of 0.5% flowing through a 1.7:1 tubular contraction. James et al. (2003)
employed a novel extensional flow apparatus to apply constant extensional strain rates in
fibre flocs. They examined softwood kraft pulp at Cm=0.01% ( 1≅N ) and found a critical
extensional strain rate of ~ 3 s-1
required to rupture these weak flocs. More recently, Yan
et al. (2006) designed a flow device to simulate the extensional flow in paper-machine
headboxes. They observed that about 20% of the flocs in a 2:1 contraction ruptured in
this extensional flow.
1.1.4. Viscoelasticity
Pulp fibre suspensions exhibit elastic as well as viscous behaviour and therefore
are considered viscoelastic. As in the case of measuring viscosity, measuring
viscoelasticity in fibre suspensions is not simple. Here too some relevant work was
carried out on suspensions of synthetic fibres.
One approach to measurement has been by normal stress differences. Nawab and
Mason (1958) were the first to observe viscoelasticity in concentrated fibre suspensions
at N>56 in the form of the Weissenberg or rod-climbing effect. Kitano and Kataoka
(1981) employed a cone-plate rheometer to study the steady shear flow properties of
suspensions composed of vinylon in silicone oil up to Cm=7%. First normal-stress
differences increased with fibre concentration, aspect ratio, and shear rate. Petrich et al.
(2000) measured the first normal stress difference of a glass fibre suspension using a
parallel-plate rheometer. They found that, for fibre suspensions, the first normal stress
difference is directly proportional to the shear rate. It is of interest to note that a similar
dependence was found between first normal stress difference and shear rate in dilute
suspensions of rigid, axisymmetric Brownian particles in a Newtonian fluid (Brenner,
1974).
Another approach to measuring viscoelasticity is by oscillatory shear. Here the
Boltzmann superposition principle is employed whereby a relaxation spectrum
determined by a single experiment for small amplitude oscillatory shear, and this is used
to determine the response in any other case (Dealy and Wissbrun, 1990). This approach is
only valid when the deformation is either small or very slow.
20
Using oscillatory strain in a parallel-plate rheometer, Swerin et al. (1992)
measured viscoelastic properties of pulp suspensions in the consistency range of 3 to 8%
in terms of storage and loss moduli. Storage and loss moduli were found to increase with
fibre mass concentration and to be independent of the applied frequency. A power-law
equation was proposed to predict the storage modulus as a function of fibre mass
concentration.
Damani et al. (1993) employed the same approach and found the elastic modulus
to be independent of the applied frequency. This is consistent with the results of Swerin
et al. (1992). The level of strain was found to have a significant effect on the elastic
modulus, especially at low fibre concentrations.
Later, Swerin (1998) examined the viscoelasticity of two fibre suspensions with
different fibre sizes (0.9 and 2.8 mm) up to Cm=1% in the presence of flocculants. All
measurements were performed in the oscillatory mode using a roughened cup-and-bob
geometry to minimize wall slippage. By measuring the variation of elastic and viscous
modulus versus straining frequency, with and without flocculants, it was shown that the
effect of flocculants on the modulus was very large because they caused significant
flocculation. The storage modulus was found to increase with increasing frequency, while
the viscous modulus was almost independent of the frequency.
Stickel et al. (2009) measured the viscoelasticity of bio-mass slurries having
average fibre lengths of 0.1 mm and aspect ratio of 1 to 20 using both parallel-plate and
vaned geometries. They found that elastic and viscous moduli depended slightly on
frequency. The elastic modulus was larger than the viscous modulus by about an order of
magnitude.
A limitation of these oscillatory methods is the use of small strains. This is likely
to produce strain and rupture between flocs rather than within them. In many processes,
flocs must be dispersed as well, and therefore this rheological measurement may have
limited value.
21
1.1.5. Fluidization of pulp suspensions
Fluidization describes a state of pulp suspensions in which elements of the
suspension move relative to one another such that the suspension adopts properties of a
fluid. An important property is pressure energy and the ability to recover this from kinetic
energy (obey the Bernoulli equation). For example, this feature permits use of centrifugal
pumps, even for medium consistency suspensions, in place of displacement pumps to
transport the suspension.
To attain fluidization, apparent yield stress must be exceeded throughout the
suspension. The stresses necessary for this pulp suspension can generally only be attained
in the turbulent state. For this reason, the terms fluidization and turbulence in pulp
suspensions are often used interchangeably.
Gullichsen and Harkonen (1981) pioneered the use of fluidization for pumping.
They determined the conditions necessary for fluidization in a rotary device. Based on
their findings, they developed a centrifugal pump capable of handling pulp suspension up
to 15% consistency. In later work a number of workers studied fluidization in more detail
(Bennington et al., 1991; Hietaniemi and Gullichsen, 1996; Bennington and Kerekes,
1996). It was found that fluidization could occur at two levels, floc level and fibre level,
because of their large difference in the apparent yield stress (Kerekes, 1983b; Bennington
et al., 1991; Hietaniemi and Gullichsen, 1996). Floc level fluidization was sufficient for
pumping, but fibre-level fluidization was necessary in some processes, for example
micro-scale mixing of fast-reacting chemicals with pulp. Both scales are commonly
found in mixing vessels as well as in other process equipment, often along with zones
having no relative velocity at all (dead spots).
Fluidization has been difficult to quantify because methods to measure velocity in
concentrated fibre suspensions are lacking. Accordingly, indirect methods have been
employed. One method is by the torque necessary to produce turbulent motion in a vessel
of prescribed dimensions (Gullichsen and Harkonen, 1981). Another is method by the
power dissipation per unit volume,F
ε , necessary for the onset of fluidization (Wahren,
1980). An issue in this characterization is the presence of large gradients of power
22
dissipation in vessels, making power dissipation equipment-specific. Bennington et al.
(1991) addressed this by determining power dissipation as a function of equipment size,
as shown by Eq. (1-11) below:
3.2
5.24105.4
−
×=
R
Tmf
D
DCε (1-11)
where 1% < Cm < 12%, DT is the outer housing diameter, DR is the rotor diameter with εf
the power dissipation/unit volume (w/m3).
Bennington (1991) observed fibre-level fluidization at the rotor vane tips and
largely floc-level fluidization in zones away from the rotor. The power dissipation at the
impeller tip was obtained by extrapolating Eq. (1-11) to zero gap size (T
D D= ). This
showed that power dissipation for fibre-level fluidization is about an order of magnitude
greater than that for floc-level fluidization in the vessel.
Other recent studies have extended knowledge of pulp suspension fluidization
(Hietaniemi and Gullichsen, 1996; Chen and Chen, 1997; Wikstrom et al., 2002). The
latter workers measured the onset of fluidization using a vaned narrow-gap viscometer,
defining the onset of fluidization as the condition at which the Power Number becomes
constant with Reynolds number (based on rotational speed) as is common for turbulent
flow in mixing vessels. They developed a correlation which gave values similar to those
of Gullichsen and Harkonen (1981), but smaller than those of Bennington et al. (1996).
This suggests that floc-level rather than fibre-level fluidization was measured.
Although fluidization generally occurs in a turbulent regime, fluid-like behaviour
at a floc level can be attained under some non-turbulent conditions. One example is the
flow induced in a rotary device at slow rotational speeds just above the apparent yield
stress (Bennington et al., 1991). Another example was found in spouted beds (van de
Ven, 2006).
23
1.1.6. Applications in pipe flow
In concluding this review chapter, it is useful to illustrate how the rheology
described above affects one of the most important flows—pipe flow. A key early study
by Robertson and Mason (1957), followed by numerous other studies cited in the review
papers in the Introduction, identified three regimes of flow behaviour which take place
with increasing velocity. These regimes give an “S” shaped friction loss curve as shown
in Figure 1-7 where pipe friction loss, ∆H (Pa), has been plotted against pipe flow
velocity, V (m/s).
At low velocity, a “plug flow” exists in which the suspension scrapes along the
wall, with some rolling of fibres at the wall (Region 1). As velocity increases, a clear
water annulus develops between the pulp plug and pipe wall (starting at peak of Region
1). Shear is concentrated in this annulus. With increasing velocity, the size of this annulus
increases in greater proportion than the velocity increase, thereby causing a decrease in
wall shear and consequently a decrease in friction loss with increasing velocity (Region 2
between peak and minimum). As velocity increases further, the annulus turns turbulent,
pulling and mixing fibres in the annulus (Region 2, minimum). This starts the “mixed
flow regime”. As velocity increases, the size of the turbulent annulus increases and the
plug core decreases. At a point in this mixed regime, the friction loss of the suspension
becomes less than that of the water flowing alone at the same rate, i.e., the flow exhibits
“drag reduction”. As velocity increases further in Region 3, eventually a fully “turbulent
regime” is attained over the whole diameter.
The above regimes occur in the low consistency range. Clearly, the range of flow
behaviour is very broad, extending from mechanical friction at the wall to turbulent drag
reduction. In the case of drag reduction, pulp fibre suspensions are one of the earliest and
most consistent solid-liquid suspensions in which this phenomenon has been observed.
The phenomenon is also found in suspensions of synthetic fibres (Kerekes and Douglas,
1972).
24
Figure 1-7: Friction loss curve for chemical pulp.
At medium consistency, suspensions are virtually always in plug flow.
Furthermore, in this range, the suspension is compressible because of its high air content,
and therefore pressure, as well as pressure difference, is important for flow. A larger
pressure causes the suspension to compress and thereby exert greater mechanical force on
the wall, which leads to greater friction loss (Longdill et al., 1988).
Attempts have been made over the years to model friction loss of pulp
suspensions in pipe flow, for example Daily and Bugliarello (1961), Luthi (1987) and
Pettersson (2004), but these have found limited use. Reasons for this are many, as
discussed in this paper and by Duffy (2003). Accordingly, predictions of friction loss in
pipe flow in the pulp and paper industry are commonly made by empirical procedures
(Duffy, 1978) that have been adopted as industry standard methods (Tappi Press TIS
0410-12).
25
1.1.7. Summary and conclusions
This chapter has described the various methods and approaches used over the
years to measure key rheological properties of pulp suspensions. Previous studies on pulp
suspension rheology are generally limited to the apparent yield stress measurements,
viscoelasticity and pipe flow experiments.
Apparent yield stress has been measured and reported for pulp fibre suspensions
using different experimental procedures and definitions. The reported values vary over a
wide range due to dissimilar definitions, different experimental approaches, and perhaps
dissimilar structural state of the suspensions used in various studies. Therefore, it is
important to study the yielding behaviour of these suspensions in a more detailed manner
to eliminate factors which may lead to dissimilar apparent yield stress values.
This literature review shows that there is little known about the flow behaviour of
pulp suspensions beyond the apparent yield stress at industrially relevant concentrations.
This is due to the difficulties associated with the experimental testing of these
suspensions. On the other hand, the lack of sufficient rheological experimental data has
led to the lack of reliable constitutive rheological models which are required to design
processing machines in the pulp industry.
Pulp suspensions are composed of fibre microstructures which evolve and/or
rupture with time and under influence of shear. This in turn makes pulp suspension a
thixotropic material with a time dependant rheological behaviour. Thixotropy and time
dependant rheology of pulp fibre suspensions should be examined in detail as there is no
study concerning these topics in the open literature.
26
1.2. Thesis Objectives
The overall objective of this research work was to first determine an appropriate
and reliable experimental approach to measure the rheological properties of pulp fibre
suspensions. Next, to implement such technique to improve our understanding on the
flow properties (rheology) of dilute and medium consistency pulp suspensions (0.5-6
wt.%) to open opportunities for applying these concepts in the pulp preparation stages in
the paper industry in the future. The particular objectives of this thesis can be
summarized as follows:
1. To determine a reliable experimental approach to study the rheology of pulp fibre
suspensions that yields consistent results (addressed in Chapters 2-4).
2. To propose a reliable technique to measure the apparent yield stress of
commercial pulp fibre suspensions that can particularly be incorporated in the
designing of mixing processes (addressed in Chapter 2).
3. To study the post yield flow behavior of various types of pulp fibre suspensions
and propose a rheological model to predict the flow behavior at steady-state
(addressed in Chapter 3).
4. To investigate effects such as thixotropy and shear banding in pulp fibre
suspensions, effects which have not been studied for pulp suspensions in the past
(addressed in Chapter 4).
1.3. Thesis Organization
The present chapter of the thesis discusses the basic motivation of the present
work. It includes a historical overview of pulp fibre suspension rheology, a brief
introduction to the terms and definitions related to pulp and paper science, and a brief
introduction into inter fibre forces and consistency ranges. In addition, this chapter
includes a review on the different experimental methods previously used for
27
measurement of pulp fibre suspension rheology and therewith identified parameters
influencing the rheology of such materials. This chapter is based on a review paper that
has been published (Derakhshandeh, B., Kerekes, R.J., Hatzikiriakos, S.G., Bennington,
C.P.J., 2011. Rheology of pulp fibre suspensions-A critical review. Chemical
Engineering Science 66(15): 3460-3470.
Chapter 2 describes a new approach to measure apparent yield stress of pulp fibre
suspensions using a velocity profile determination technique coupled with a rheometer.
Unlike previous approaches, which assumed the nature of velocity profiles in the
rheometers, this approach measures the velocity profiles directly and links them to the
shear stress evolution in the suspension, thereby measuring the apparent yield stress. The
experimental techniques used in this research work and the pulp suspension preparation
procedures are described in this chapter in detail. This chapter is based on a journal paper
that has already been published (Derakhshandeh, B., Hatzikiriakos, S.G., Bennington,
C.P.J., 2010. The apparent yield stress of pulp fibre suspensions. Journal of Rheology
54(5): 1137-1154).
Chapter 3 studies the behaviour of pulp fibre suspensions beyond the apparent
yield stress. Conventional rheometry and a velocity profile determination technique have
been used and the obtained results are compared. Models have been proposed to describe
the flow behaviour using the local velocity profiles within the rheometer. Effects of lignin
content and pH on the rheology of pulp fibre suspensions have also been discussed. This
chapter is based on a journal paper that has already been published (Derakhshandeh, B.,
Hatzikiriakos, S.G., Bennington, C.P.J., 2010. Rheology of pulp fibre suspensions using
ultrasonic Doppler velocimetry. Rheologica Acta 49(11-12): 1127-1140).
Chapter 4 studies thixotropy and transient behaviour of pulp fibre suspensions. A
velocity profile determination technique is used to measure velocity profiles within the
suspension at steady-state and transient flow conditions. The effects of rest time and
shear history are studied and mechanisms of structure build-up and breakdown are
discussed. Moreover, the possibility of shear-banding instability in concentrated pulp
suspensions is examined and models have been proposed to describe the flow of
concentrated pulp fibre suspensions. This chapter is based on a manuscript that has been
28
submitted for publication (Derakhshandeh, B., Vlassopoulos, D., Hatzikiriakos, S.G.,
2011. Thixotropy, yielding and ultrasonic Doppler velocimetry in pulp fibre suspensions.
Rheologica Acta).
Finally, the conclusions, contributions to knowledge and recommendations for
future research are summarized in chapter 5. A general summary of the most significant
findings from this work is also presented.
29
2. The Apparent Yield Stress of Pulp Fibre
Suspensions2
2.1. Introduction
Pulp fibre suspensions consist of fibre networks having considerable strength.
Before they begin to flow, a minimum shear stress must be applied to disrupt the fibre
networks referred to as the yield stress. We will refer to this quantity as apparent yield
stress since different methods may result in different values. Despite the controversial
concept of the yield stress as a true material property (Scott, 1933; Barnes and Walters,
1985) the apparent yield stress is considered as one of the most important rheological
properties of pulp fibre suspensions in designing process equipment for the pulp and
paper industry.
As discussed in chapter 1, several methods and definitions have been
proposed/developed to predict and measure the apparent yield stress both directly and
indirectly (Pryce-Jones, 1952; Head and Durst, 1957; Thalen and Wahren, 1964; Van den
Tempel, 1971; Papenhuijzen, 1972; Duffy and Titchener, 1975; Nguyen and Boger, 1992;
Liddell, 1996). These methods make use of various pieces of equipment such as a
concentric cylinder shear tester (Gullichsen and Harkonen, 1981), a rotary shear tester
(Bennington et al., 1990) and a reservoir-type parallel plate geometry (Damanai et al.,
1993; Swerin et al., 1993; Wikström et al., 1998). In addition to experimental studies,
models of the form b
my aC=σ have been proposed to represent the apparent yield stress
as a function of mass concentration (Meyer et al., 1964; Kerekes et al., 1985; Bennington
et al., 1990; Bennington et al., 1995).
Pulp rheological characterization is no easy task due to the unique and complex
behaviour of wood fibre suspensions described in chapter 1. Pulp suspensions consist of
roughly cylindrical fibres of average length ranging from 1 mm to 3 mm having aspect
ratios of 40 to 100. Fibres entangle mechanically to form regions of higher fibre mass
2 A version of this chapter has been published. Derakhshandeh, B., Hatzikiriakos, S.G., Bennington, C.P.J.,
2010. The apparent yield stress of pulp fibre suspensions. Journal of Rheology 54(5): 1137-1154.
30
concentrations of average size of 2 cm to 3 cm referred to as fibre flocs (Mason, 1950;
Stockie, 1997).
Increasing the fibre concentration, the number of fibre-fibre contacts increases
which results into formation of network structures throughout the suspension (Kerekes
and Schell, 1992). Presence of individual fibres, fibre flocs and networks makes pulp
fibre suspensions heterogeneous and multiphase systems. This is against the basic
homogeneity assumption which is made to predict simple fluid flow characteristics. The
presence of millimetre-sized fibres and centimetre-sized fibre flocs in a heterogeneous
suspension makes it complicated to obtain reproducible rheological data. Pulp
suspensions contain a dispersed phase with dimensions comparable to the characteristic
dimensions of the geometry of the measuring apparatus in rheological devices and
therefore fibre rotation is limited.
Another common behaviour of pulp fibre suspensions is their orientation around
the measuring elements and migration of fibres away from solid boundaries which leads
to formation of a depletion layer that complicates further rheological measurements
(Nguyen and Boger, 1992; Barnes, 1995; Swerin, 1998; Wikström, 1998; Archer, 2005).
Due to these complications and those discussed in chapter 1, the selection of an
appropriate measuring device to provide large measurement gaps (compared with the
dimensions of the fibre domains to eliminate fibre jamming) as well as decrease the
possibility of apparent slip at solid boundaries is required to obtain reliable data.
Various methods have been proposed in the literature to interpret the rheological
data which are affected by wall slip, particularly for foams, emulsions and polymers
(Mooney, 1931; Jastrzebski, 1967; Yoshimura and Prud’homme, 1988; Hatzikiriakos and
Dealy, 1991). These corrections cannot be applied to raw rheological data obtained from
pulp suspensions. For instance, Yoshimura and Prud’homme (1988) considered the wall
slip to be a function of wall shear stress and proposed a method to correct the rheological
data by examining the dependency of the rheological data on the gap size in a parallel-
plate geometry. Decreasing the gap size in the case of pulp suspensions squeezes water
out, and, as a result, the fibre mass concentration increases. This leads to imprecise
rheological data.
31
Another approach to minimize the effect of slip is to make use of complex
geometries such as the vane geometry (Nguyen and Boger, (1983, 1985); Barnes et al.,
1990; Barnes et al., 2001; Cullen et al., 2003). Vane geometry is basically a small shaft
with a small number of thin blades (usually 2-8) arranged at equal angles. Application of
the vane geometry requires that a number of assumptions be made. First, it is assumed
that the fluid in between the blades rotates along with them so that it generates a
cylindrical surface with a radius close to that of the vane. It has been shown that this
assumption is valid for highly shear-thinning fluids with power-law indices less than 0.5.
In this case little or no shearing occurs in between the blades of the vane. Therefore, the
fluid is sheared at the virtual cylinder prescribed by the tips of the vane blades (Barnes
and Carnali, 1990). Second, the shear stress distribution is assumed to be uniform at the
outer virtual cylindrical surface described by the outer edge of the vane and finally, the
fluid which is trapped between the blades of the vane is assumed to act as a rigid body
without any secondary flow.
These assumptions are valid in vanes with four or more blades (Nguyen and
Boger, 1983). Despite these assumptions, the vane geometry has many advantages over
the other geometries. Particularly, when used to study complex systems such as pulp
suspensions. In a vane geometry, the fluid is sheared within itself. Therefore, the wall
slippage is minimized (Barnes and Nguyen, 2001). In addition to the decrease of the wall
slip, insertion of the vane generates the least amount of disturbances to the structure of
the sample although it can be significant, particularly in the case of thixotropic fluids
(Nguyen and Boger, 1983).
Most commercial rheometers utilize narrow gaps which impose practical
restrictions to sample rheological behaviour. These include fibre jamming, tumbling,
orientation and the formation of depletion layers. Vane geometry with large cups
provides wide gaps which enable the investigation of fluids containing large particles or
fibres that can exhibit considerable apparent wall slip (Bennington et al., 1990; Zhang et
al., 1998; Baravian et al., 2002; Martin et al., 2005; Ramírez-Gilly et al., 2007).
A significant amount of discrepancy can be found among the reported apparent
yield stress values (Gullichsen and Harkonen, 1981; Bennington et al., 1990; Swerin et
32
al., 1993; Damani et al., 1993; Wikström et al., 1998; Ein-Mozaffari et al., 2005). An
example is given in Table 1-1, where the reported values for the apparent yield stress of a
3 wt.% bleached softwood kraft pulp range from 19.3 to 350 Pa, while those of a 6 wt.%
range from 60 to 1220 Pa. These discrepancies are due to differences in pulp type, the
way the apparent yield stress is defined and the technique used to measure it.
As discussed in chapter 1, the apparent yield stress can be measured by means of
either stress-controlled or rate-controlled rheometers by performing creep or steady shear
tests respectively. Using a rate-controlled rheometer and applying a constant strain rate,
the shear stress can be measured as a function of strain or time. The apparent yield stress
can then be calculated as the maximum shear stress measured, the steady-state shear
stress or the shear stress at which departure from linearity begins (very difficult to
establish uniquely). Each of these definitions gives a different value for the apparent yield
stress (Thalen and Wahren, 1964; Nguyen and Boger, 1985; Liddell and Boger, 1996).
Another approach is to apply a slow shear rate ramp to obtain the variation of
torque as a function of rotational speed. The apparent yield stress is calculated using the
maximum torque measured during the experiment (Bennington et al., 1990). Using a
stress-controlled rheometer and increasing the shear stress in a linear manner, the
variation of the instantaneous viscosity (instantaneous shear stress divided by the
instantaneous shear rate) versus shear stress can be obtained. The apparent yield stress is
the value at which the instantaneous viscosity drops significantly or is a maximum
(Cheng, 1986; Zhu et al., 2001; Brummer, 2005; Coussot, 2005; Nguyen et al., 2006).
The main objective of this chapter is to identify a reliable technique for measuring
the apparent yield stress of pulp fibre suspensions that yields consistent results. To
establish this technique, the apparent yield stress of several commercial pulp fibre
suspensions over a wide range of mass concentrations is measured by using conventional
apparent yield stress measurement methods utilizing both a stress-controlled and rate-
controlled rheometer. The apparent yield stress values obtained using these techniques
are compared with those obtained from a velocity profile determination technique using
ultrasonic Doppler velocimetry (described in the next section). The reliable data from this
33
comparison are used to obtain models for the apparent yield stress of pulp fibre
suspensions.
2.2. Velocity Profile Determination Using Ultrasonic
Doppler Velocimetry
While conventional rheometry is the most widely used technique for rheological
characterization, fluid visualization methods have also been found useful in rheology
(Takeda, 1986; McClements et al., 1990; Bachelet et al., 2004; Be´cu et al., 2006; Koseli
et al., 2006).
These techniques primarily make use of light to measure instantaneous velocities
in a flowing fluid. Among others, Particle Image Velocimetry (PIV) and Laser Doppler
Velocimetry (LDV) are the most common ones in fluid flow measurements. In these
techniques, fluid is often seeded with tracer particles which are assumed to follow the
fluid flow dynamics. Tracking the motion of the seeded particles, the fluid velocity can
be obtained instantaneously. These two techniques often require a complicated set-up and
as they utilize laser light to follow the flow field they are exclusive to the transparent
systems. Therefore, in the case of opaque systems such as pulp fibre suspensions other
techniques such as ultrasonic Doppler velocimetry (UDV) should be implemented.
Ultrasonic Doppler velocimetry (UDV) is a simple, non-intrusive acoustic
measurement technique based on the Doppler effect (more detail can be found in
Appendix A). In this technique, a short ultrasonic burst with an angle θ0 relative to the
normal to the wall is sent to the fluid periodically and the echoes issuing from the
suspended particles are collected (Figure 2-1). However, as the ultrasound travels through
the wall, the initial angle θ0 changes to θ the value of which is given by the law of
refraction (Manneville et al., 2004). Using the time delay, tf, and the frequency shift of
the reflected pulses, fd, the location and the velocity of the particles in the direction of the
acoustic axis are obtained using Eqs. (2-1) and (2-2) (Hein and O’Brien, 1993).
2
fcty = (2-1)
34
θcos2)(
0f
cfyu d= (2-2)
where c is the sound velocity in the medium, f0 is the ultrasound emission frequency and
θ is the emission angle into the fluid.
The radial position and the orthoradial velocity of the reflecting particles in
Couette geometry can then be found by using Eqs. (2-3) and (2-4) based on the geometry
shown in Figure 2-1 (Manneville et al., 2004).
)(sin
)(2
yuR
rru
θ= (2-3)
θcos2 2
22
2 yRyRr −+= (2-4)
Figure 2-1: Ultrasonic Doppler velocimetry in Couette geometry. r is the radial distance
from the rotor, y is the distance from the outer wall along the acoustic axis and Ry is the
yielding radius.
As UDV measures accurately the velocity profiles of a flowing fluid, it can be
coupled with conventional rheometers to study the rheological behaviour of complex
35
fluids in a more precise manner. Particularly, when coupled with a Couette geometry, the
torque T imposed on the moving cylinder by the rheometer yields the stress distribution
σ(r) across the gap, while the velocity profile obtained by UDV permits determination of
the local shear rate )(rγ& according to Eqs. (2-5) and (2-6) (Bird et al., 2001).
22
)(rh
rπ
σΤ
= (2-5)
∂
∂−=
r
u
rrr
r )()(γ& (2-6)
where h is the cylinder height., 1R is the cylinder radius, R2 is the cup radius with
21 RrR ≤≤ (Figure 2-1).
By using large gaps to study the rheological properties of viscoplastic fluids that
exhibit an apparent yield stress, such as paper pulps, polymers and ceramic pastes, the
vane creates a sheared (yielded) zone within which the material is in flow. However, as
the shear stress falls below the apparent yield stress, the flow stops generating an un-
yielded zone, i.e. the velocity is practically equal to zero between Ry and R2 (Figure 2-2).
By knowing the radius of shearing Ry obtained using UDV measurements and the
steady-state shear stress at the vane surface σT obtained using the torque reading from the
rheometer, the apparent yield stress yσ can be calculated from Eq. (2-7) (Fisher et al.,
2007).
2
1
=
y
TyR
Rσσ (2-7)
36
Figure 2-2: Schematic of vane in large cup geometry with yielded and un-yielded
regions.
2.3. Materials and Experimental Testing
Pulp fibre suspensions were prepared from bleached softwood kraft (SBK) and bleached
hardwood kraft (HW) (Domtar Inc., Windsor, QC), thermal-mechanical-pulp (TMP)
(Howe Sound Pulp and Paper Limited Partnership, Port Melon, BC) and stone-ground
wood (SGW) (Paprican, Pointe-Claire, QC) by breaking up the dried pulp sheets and
rehydrating the fibres with tap water using a disintegrator (TMI, Montreal, QC) for 30
minutes at 120 rpm. Suspensions of 0.5, 1.0, 2.0, 2.5, 3.0, 4.0 and 5.0 wt.% were
prepared. The pulp fibre properties are summarized in Table 2-1. The mean fibre length is
an important parameter as shown below. In this study, it varies from 0.67 to 2.96 mm
(Table 2-1). Fibre Curl Index is the ratio of actual fibre length to the distance between the
2 fibre ends minus 1. It indicates the continuous curvature of the fibres greater than 0.5
mm in length and within the selected range limits. Fibre Kink Index is the sum of the
number of kinks (an abrupt change in fibre curvature) within a range of kink angles
divided by the total fibre length of all the fibres.
37
Table 2-1: Properties of pulp fibres used in the present study
Fibre
System
Fibre Properties
Mean length
Lw (mm)
Percent fines
(L=0.07-0.2
mm)
Mean
curl
index
Mean
kink index
SBK 2.96 1.9 0.27 2.11
HW 1.28 8.17 0.105 1.98
TMP 1.36 11.9 0.05 0.50
SGW 0.67 23.1 0.09 1.43
A four-bladed vane, 38.5 mm in height and 25 mm in diameter, was placed in a
transparent cylindrical cup having an internal diameter of 100 mm and a height of 64 mm
resulting in a gap size of 37.5 mm. To obtain consistent rheological data for pulp
suspensions and to eliminate shear history after loading the sample into the measuring
device, all samples should have the same structural state prior to experimental testing. To
achieve this, the suspension should be pre-sheared with a preset shear stress or shear rate
over a fixed time span in order to rupture most of the fibre structures. The suspension
should then be kept at rest for another specific period of time to recover its structure to a
certain level for all subsequent experiments. The effectiveness of the pre-shearing
conditions can be examined by checking the dependency of the viscosity on the shear rate
after applying the pre-shearing conditions. The optimum pre-shearing conditions are
those for which different samples of the same suspension exhibit the same viscosity
versus shear rate relationship.
Given this, a series of tests was conducted to determine the optimum pre-shearing
conditions for each sample. Tests were performed at each suspension mass concentration
with different levels of shear stress applied for different lengths of time. Samples were
then redistributed evenly in the gap and left to rest for 15 minutes followed by checking
the dependency of the viscosity on the shear rate. The optimum pre-shearing conditions
were identified as those for which different samples exhibited the same viscosity-shear
rate relationship. These conditions were then used in all subsequent tests (Table 2-2).
The apparent yield stress values of the pulp suspensions were measured using
three methods. In the first, a stress-controlled Bohlin C-VOR rheometer (Malvern,
Worcestershire, UK) was used to linearly increase the shear stress in steps and the
38
variation of the instantaneous viscosity (instantaneous shear stress divided by the
instantaneous shear rate) versus shear stress was obtained. The apparent yield stress was
measured as the stress value for which the instantaneous viscosity exhibited a maximum
(Cheng, 1986; Zhu et al., 2001; Brummer, 2005; Coussot, 2005; Nguyen et al., 2006).
Table 2-2: Optimum pre-shearing conditions applied on pulp suspensions
Cm SBK HW TMP SGW
σ(Pa) t(s) σ(Pa) t(s) σ(Pa) t(s) σ(Pa) t(s)
0.01 50 10 15 5 10 10 5 5
0.02 120 15 40 10 45 10 50 10
0.025 230 20 80 20 72 10 80 15
0.03 300 20 125 30 95 30 75 15
0.04 460 30 200 30 240 40 170 35
0.05 580 40 365 35 350 40 260 40
The second method used a rate-controlled Haake RV12 Rotovisco viscometer
(Thermo Fisher Scientific Inc., Waltham, MA) at a rotational speed of 8 rpm. For this
experiment the torque–time response was measured with the peak torque used to
calculate the apparent yield stress. This technique has commonly been used to measure
the apparent yield stress of various substances (Cadling and Odenstad, 1950; Donald et
al., 1977; Bowles, 1977; Nguyen et al., 1981; Nguyen and Boger, 1983; Ein-Mozaffari et
al., 2005).
The third method used the Haake RV12 viscometer at two rotational speeds of 8
and 16 rpm and a pulsed ultrasonic Doppler velocimeter (Model DOP2000, Signal
Processing, Switzerland) to measure the velocity profiles across the gap. The ultrasonic
transducer has an active diameter of 20 mm and a pulse repetition frequency of 100 Hz to
15.6 KHz which can be changed depending on the magnitude of the expected velocity. A
cup, identical to those used in the other methods, was made with an indentation of 14° at
the surface to attach the UDV probe. The space between the transducer and the Plexiglas
wall was filled with an ultrasonic gel to establish an efficient acoustic coupling between
the probe and the vessel. The Plexiglas interface between the transducer and suspension
was machined as thin as possible so that the refraction of the beam due to the interface
can be neglected i.e. θ0~θ in Figure 2-1.
39
2.4. Results and Discussion
2.4.1. Apparent yield stress measurement by linear stress ramps
Figure 2-3 depicts a typical apparent yield stress measurement for a 1 wt.%
bleached softwood kraft pulp suspension at 23°C. Measurements were performed at least
five times to check the reproducibility and minimize experimental error.
Figure 2-4 shows the typical behaviour of the transient strain )(tγ when shear
stresses lower and greater than the apparent yield stress are applied to the pulp
suspension. For stresses lower than the apparent yield stress an initial jump in strain
(elastic response) was observed followed by a gradual increase in the strain until reaching
a constant value (solid-like behaviour). For stresses above the apparent yield stress value,
the strain increases monotonically, reaching a constant slope (fluid-like behaviour).
Figure 2-3: Repeats of apparent yield stress measurements for a bleached softwood kraft
pulp suspension (SBK) of mass concentration of 1 % at 23 °C applying a linear shear
stress ramp.
40
Figure 2-4: Creep response of a bleached softwood kraft pulp suspension (SBK) of mass
concentration of 1 % at 23 °C for shear stress values lower and higher than the apparent
yield stress. Note that pulp suspension exhibits a solid behaviour below the apparent yield
stress while a fluid behaviour can be observed above the apparent yield stress.
The apparent yield stress values obtained by applying linear shear stress ramps are listed
in Table 2-3 and plotted in Figure 2-5 as a function of mass concentration.
Table 2-3: Apparent yield stress values obtained by using the linear shear stress ramp method
Cm
Apparent Yield Stress (Pa)
SBK HW TMP SGW
0.005 2±0.60 0.33±0.1 0.18±0.05 0.11±0.03
0.01 13±4 4±1.5 1±1 0.73±0.1
0.02 57 ±6 14±2 16±3 9±1
0.025 114±16 26±4 27±1 17±1
0.03 154±13 48±8 50±11 28±4
0.04 242±45 80±10 125±12 69±2
0.05 384±49 166±7 245±32 150±9
The dependency of the apparent yield stress values on fibre mass concentration
has been correlated using a power-law model (b
my aC=σ ). The resulting fitted constants
are listed as an insert in Figure 2-5. These are within the range of previously reported
results (Kerekes et al., 1985).
41
Figure 2-5: The apparent yield stress values of all tested pulp suspensions as a function
of mass concentration obtained by using the shear stress ramp method at 23 °C.
The measured apparent yield stress values depend on the physical properties of
the fibres. Fibres tend to form networks due to a number of attractive forces. These
include colloidal, mechanical surface linkage, elastic fibre bending and surface tension,
although mechanical entanglement is the greatest (Kerekes et al., 1985). Fibre properties,
such as fibre length, flexibility and elastic modulus contribute to these forces and affect
the apparent yield stress of the suspension. More flexible and longer fibres permit greater
contact between adjacent fibres, increase the number of mechanical linkages and
therefore the apparent yield stress. Due to differences in fibre length and flexibility, the
apparent yield stress decreases from SBK > TMP ≅ HW > SGW at a given mass
concentration. Increasing suspension concentration increases the number of fibre
entanglements, the strength of the fibre network formed and hence the apparent yield
stress as shown in Figure 2-5 for all the pulp suspensions tested.
42
2.4.2. Apparent yield stress measurement by the start-up of
shear flow experiment
Apparent yield stress measurements were also performed using start-up of steady
shear experiments in the Haake RV12 rheometer. Each experiment was performed five
times and the apparent yield stress values were measured as the maximum shear stress
achieved in the shear stress vs. time response. Typical measurements are plotted in Figure
2-6 for a 3 wt.% bleached softwood kraft pulp suspension. The apparent yield stress
values obtained using this technique are listed in Table 2-4.
Generally, these values were larger than those obtained by using the previous
(linear shear stress ramp) method, although the same trend as a function of fibre type and
mass concentration was observed (Figure 2-7). The resulting fitted constants to power
law model (b
my aC=σ ) are also listed in the insert of Figure 2-7.
Figure 2-6: Stress response after imposition of steady shear at vane rotational rate of 8
rpm for a 3 wt.% bleached softwood kraft pulp suspension (SBK) at 23 °C. Multiple tests
indicate the level of reproducibility.
43
Table 2-4: Apparent yield stress values obtained by using the start-up of steady shear flow
experiment
Cm
Apparent Yield Stress (Pa)-Controlled Rate-
RPM=8
SBK HW TMP SGW
0.005 5±1.6 1.5±0.1 0.85±0.4 0.14±0.03
0.01 39±2 9±4 4±2 3±1
0.02 105 ±6 30±8 33±10 35±9
0.025 205±16 55±23 53±16 48±23
0.03 248±40 87±31 65±25 55±17
0.04 388±58 151±40 180±45 118±38
0.05 518±60 292±52 289±42 196±34
Figure 2-7: The apparent yield stress values of all tested pulp suspensions as a function
of mass concentration obtained by applying the start-up of steady shear flow at 23 °C.
Under the application of constant rotational rates (constant shear rates),
viscoelastic thixotropic fluids exhibit an initial stress growth that is followed by a slight
stress decay to a final stead-state value. However, pulp suspensions do not attain an
ultimate constant shear stress; instead they exhibit an oscillatory behaviour as shown in
44
Figure 2-6. This characteristic is due to the complex behaviour of fibre flocs during flow.
In flow, some flocs tend to move along with the vane but slow down as the contact with
the vane tip is lost. As a floc moves along with a blade, the required shear stress to
maintain constant rotational rate increases. On the other hand, stress decreases when a
floc loses contact with the blade tip. Due to this behaviour the shear stress does not reach
a “true” steady-state value.
2.4.3. Apparent yield stress measurement by ultrasonic Doppler
velocimetry (UDV)
An ultrasonic Doppler velocimeter was used to determine the velocity profile in
the gap of various pulp suspensions in conjunction with torque measurements made with
the Haake RV12 rotovisco viscometer. Two constant vane rotational rates of 8 and 16
rpm were used. The UDV probe was adjusted to 14° so that velocity measurements could
be made at the tip of the rotating vane. Velocity profiles for different pulp suspensions at
the rotational rate of 8 rpm are presented in Figures 2-8a-8d.
45
46
Figure 2-8: Velocity profiles across the gap for, a) SBK, b) HW, c) TMP, d) SGW pulp
suspensions, at 23 °C and several mass concentrations. Note that the apparent yield stress
increases nonlinearly with increase of the mass concentration and thus the yielding radius
decreases.
The velocity decreases across the gap from a maximum value at the vane tip and
drops to zero at a certain distance which is referred to as yielding radius Ry (Figure 2-2).
The shear stress decreases in the gap according to Eq. (2-5). The suspension
contained in the region between the vane tips and the yielding radius is in flow, while the
fluid beyond this region remains stationary. Increasing the mass concentration of pulp
suspension increases the apparent yield stress and decreases the yielding radius, while the
velocity profiles tend to move closer to linearity (Figures 2-8a-8d).
The yielding radius and the steady-state shear stress at the vane were used to
calculate the apparent yield stress of suspensions by using Eq. (2-7). The results are
summarized in Table 2-5 and depicted in Figure 2-9 with power-law fits to the data.
47
Table 2-5: Apparent yield stress obtained using UDV coupled with a rate-controlled viscometer
Cm
Apparent Yield Stress (Pa)-Velocity Profile
Determination Technique
SBK HW TMP SGW
0.005 1±0.6 0.2±0.1 0.24±0.05 0.08±0.03
0.01 11±2.5 3±1.5 1.7±0.6 0.47±0.1
0.02 46±11 11±2.4 14±3 8±1
0.025 105±21 20±5.3 25±5 15±3
0.03 137±18 40±12 45±11 23±4
0.04 221±45 71±54 118±21 56±13
0.05 358±49 181±62 238±54 127±35
Figure 2-9: The apparent yield stress values of all tested pulp suspensions as a function
of mass concentration obtained using local velocity profile measurements at 23 °
C, at a
constant rotational rate of 8 rpm, at pulsed repetition frequency of 8000 Hz and incident
angle of 14°.
In an ideal yield stress fluid, the shear rate and thus the mean velocity must
decrease gradually from a maximum value at the tip of the vane towards zero at the
yielding radius. As seen in Figures 2-8a-8d, in pulp suspensions of higher mass
concentrations depending on the pulp fibre properties (flexibility, size, etc.) the mean
48
velocity decreases from a maximum at the tip of the vane and suddenly drops to zero at
the yielding radius resulting a discontinuity in the velocity profiles during the transition
from the yielded to the un-yielded region. This behaviour has also been observed in
concentrated colloidal suspensions, referred to as shear-banding or shear-localization
effect which results from yielding and the thixotropic characteristics of the fluid. In this
case, rheological models such as Bingham, Casson and Herschel-Bulkley do not predict
the velocity profiles accurately and the apparent yield stress of the fluid depends on the
procedure for determining it (Coussot et al., 2002a).
Pulp suspensions are heterogeneous systems containing millimetre-sized fibres
and centimetre-sized fibre flocs. The discontinuity in the velocity profiles at the transition
from the yielded to the un-yielded zone can also be due to the existence of large moving
flocs in the layer next to the un-yielded zone. In this case, UDV identifies finite velocities
for the moving fibre flocs dropping to zero in the next layer. Therefore, at this point it is
not clear, whether pulp suspensions display shear localization or banding as they go
through the yielding transition. Shear-Banding in concentrated pulp fibre suspensions is
studied in detail in chapter 4.
2.4.4. Comparison of the different apparent yield stress
measurement methods
A comparison of the apparent yield stress values determined using each method is
given in Figures 2-10a-10d for the pulp suspensions studied with the constants fitted to
the power law model summarized in Table 2-6. There is satisfactory agreement between
the apparent yield stress values obtained using the linear shear stress ramp and the
velocity measurement techniques, while the apparent yield stress values obtained using
start-up of shear flow method have considerably larger values.
49
50
Figure 2-10: Comparison of the apparent yield stress values obtained using three
different methods for a) SBK, b) HW, c) TMP, d) SGW pulp suspensions, at 23 °C and
several mass concentrations. Note that the apparent yield stress values obtained by using
the linear shear stress ramp and the velocity profile determination techniques are in good
agreement.
51
Fibre networks consist of large flocs attached to each other by weaker fibre
networks. Application of a constant shear stress in pulp breaks the weaker bonds in
between different flocs and the suspension’s behaviour deviates from that of an elastic
solid (departure from linearity in the shear stress-time data). This deviation possibly
occurs at a shear stress where the instantaneous viscosity is maximum. This regime which
occurs at low shear stresses is referred to as the macro-scale deformation regime
(Wikström, 2002). The critical shear stresses for the onset of deviation from the linearity
in the shear stress-time data would have resulted in values closer to those determined by
the shear stress ramp. However, it is difficult to accurately establish such critical stresses
experimentally; this is the reason why these values are not reported in the present work.
With further increase in the shear stress, the yielded area increases and weaker
fibre flocs possibly begin to rupture (Steen, 1990). This regime is referred to as the
micro-scale deformation regime (Wikström, 2002). Beyond a specific shear stress
(equivalent to the maximum shear stress in the start-up of shear experiment), most of the
fibre flocs move freely in the suspension. This results in higher values of the apparent
yield stresses compared with those obtained by the other methods.
As the velocity profile measurement technique uniquely identifies the velocity
distribution and yielding radius in the gap, this technique gives a more accurate
determination of the apparent yield stress. However, this technique is time consuming
and not convenient compared with macroscopic rheometry as the application of equations
must be made to infer the rheological properties from the velocity profiles. When
applying a constant shear rate, the shear stress increases rapidly which ruptures the fibre
network abruptly. Therefore, the accuracy of the apparent yield determination decreases.
However, by increasing the shear stress or the shear rate slowly, the fibre network
ruptures gradually making it easier to determine the shear stress at which flow begins.
Since the apparent yield stress values obtained using the linear shear stress ramp method
are in good agreement with those obtained by the velocity measurement technique,
applying linear shear stress ramps by using a stress controlled rheometer is an easy and
reliable alternative for apparent yield stress measurements.
52
Table 2-6: Summary of fitted constants to the power-law model (b
my aC=σ ) for all tests
Pulp
Type
Mass Fraction
Range Used
Linear Shear Stress Ramp Method Constant Shear
Rate Method
Velocity Profile Determination
Method
a×10-5
b Goodness
of Fit
a×10-5
b Goodness
of Fit
a×10-5
b Goodness
of Fit
SBK 0.005≤Cm≤0.05 4.95±0.20 2.33±0.10 0.99 2.22±0.15 1.95±0.11 0.98 8.10±0.50 2.50±0.13 0.98
HW 0.005≤Cm≤0.05 3.94±0.23 2.60±0.21 0.98 1.22±0.10 1.12±0.10 0.98 7.25±0.70 2.80±0.21 0.98
TMP 0.005≤Cm≤0.05 35.2±2.22 3.18±0.25 0.99 1.80±0.15 2.17±0.20 0.97 20.0±0.18 3.00±0.25 0.97
SGW 0.005≤Cm≤0.05 19.0±0.96 3.16±0.16 0.96 32.0±1.9 3.10±0.15 0.96 26.0±0.13 3.26±0.13 0.98
53
2.5. Summary
Pulp fibre suspensions are composed of fibre networks and flocs which possess
measureable apparent yield stress. The two most widely used apparent yield stress
measurement methods are linear shear stress ramps and start-up of steady shear flow
experiments. These were used in this study to measure the apparent yield stress of
different pulp fibre suspensions at low fibre mass concentrations up to 5 wt.%. Results
obtained using these techniques differed significantly from each other. To determine the
most reliable technique, an ultrasonic Doppler velocimeter (UDV) was coupled with a
rate-controlled rheometer to provide a robust device and reliable method which can be
used to measure the apparent yield stress. By explicitly determining the velocity profiles,
the results from this technique were found to be in agreement with those obtained from
the linear shear stress ramp method. Therefore, this technique can be used to obtain
experimental data safely and efficiently.
54
3. Rheology of Pulp Suspensions Using Ultrasonic
Doppler Velocimetry3
3.1. Introduction
Complex materials such as colloidal suspensions, foams, emulsions, fibre
suspensions and gels are widely used materials in many industrial applications
(Bennington et al., 1990; Bergenholtz et al., 2002; Stickel et al., 2009). These materials
are composed of particles/fibres, which interact with each other physically and/or
chemically while dispersed in a continuous aqueous medium. Due to these interactions
they often exhibit unusual rheological behaviour, which makes their rheological study a
nontrivial task (Larson, 1998).
Pulp fiber suspensions fall into the category of complex fluids described above.
Pulp fibre suspension flows, despite their extensive importance, have received limited
attention due to the difficulties associated with appropriate experimental measurements,
their heterogeneous nature and the lack of a general standard experimental procedure
(Bennington et al., 1990; Swerin et al., 1993; Wikström et al., 1998).
Previous studies on pulp suspension rheology are mostly limited to apparent yield
stress measurements (Gullichsen and Harkonen, 1981; Bennington et al., 1990; Swerin,
1993; Wikström et al., 1998), viscoelasticity studies (Damani et al., 1993; Swerin, 1993;
Swerin et al., 1998) and pressure-driven pipe flow experiments (Lee and Duffy, 1976;
Logdill et al., 1988; Ogawa et al., 1990; Li et al., 1995b; Duffy and Abdullah, 2003;
Duffy et al., 2004). The behavior of pulp suspensions beyond apparent yield stress has
received little attention in the literature. However, this behavior is of great importance
since all processes in the pulp and paper industry occur at high shear stresses. Having
consistent rheological data, i.e., complete flow curves, more practical, precise and reliable
rheological models can be proposed.
3 A version of this chapter has been published. Derakhshandeh, B., Hatzikiriakos, S.G., Bennington, C.P.J.,
2010. Rheology of pulp fibre suspensions using ultrasonic Doppler velocimetry. Rheologica Acta 49(11-
12): 1127-1140.
55
Wood fibres are held tightly together by a chemical substance referred to as
lignin. Wood chips are processed in order to liberate the wood fibres from lignin during
pulping process so they can be used to make paper products. Breaking down the wood
into fibres can be accomplished by mechanical or chemical processes or combinations of
both. These treatments alter the fibre properties, the fibre lignin content and the fibre
geometric dimensions such as the diameter, length and fibre wall thickness (Smook,
1992; Biermann, 1996; Gullichsen and Fogelholm, 1999). These changes in fibre
properties in turn affect the flow behaviour of pulp suspensions. To optimize various
processes and process equipment in the pulp industry, it is necessary to understand the
effects of such parameters on the rheology of fibre suspensions.
This chapter demonstrates that conventional rheological measurement techniques
fail when used to study complex fluids such as pulp fibre suspensions. In addition, it is
shown that the velocity profile determination techniques, when coupled with
conventional rheometry, make a robust apparatus to investigate the rheological properties
of such complex fluids.
We first study the steady-state flow curves of different types of pulp suspensions
over a wide range of fibre mass concentration using conventional rheometry techniques.
Next, ultrasonic Doppler velocimetry (UDV) is coupled with conventional rheometry to
study the same suspensions. The effective rheological behavior of pulp suspensions are
then inferred from these local measurements and compared with those deduced from
conventional experiments. A Herschel-Bulkley model is used to fit both the velocity
profiles obtained by coupled UDV-rheometry technique and the steady-state flow curves
obtained by conventional rheometry. Finally, the effect of pH and lignin content
(important parameters during the process of pulp fibre production) on the final
rheological behavior of pulp fibre suspensions at different fibre mass concentrations are
studied. Two types of pulp suspensions, one without lignin (softwood bleached kraft) and
the other with lignin (thermal-mechanical pulp) at different fibre mass concentrations and
pH levels are examined.
56
3.2. Materials and Experimental Testing
Pulp fibre suspensions were prepared at fibre mass concentrations of 1 to 5 wt.%
using the procedure explained in section 2.3 of chapter 2. Hydrochloric acid and sodium
hydroxide solutions of 0.1N were used to adjust the pH of 1, 3 and 5 wt.% SBK and TMP
pulp suspensions at 4, 6, 8 and 10. Pulp suspensions were kept at these pH levels for 24
hours prior to the experimental testing.
To obtain the steady-state flow curves of pulp suspensions, conventional
rheometrical tests were carried out with a stress-controlled Kinexus rotational rheometer
(Malvern instruments Ltd, UK). Constant shear stress values were applied on the
suspensions and the steady-state shear rate values were obtained. The flow curves were
then constructed using data points obtained by the creep tests from a similar vane in large
cup geometry to that described in chapter 2.
A Haake RV12 viscometer was coupled with a pulsed ultrasonic Doppler
velocimeter (Model DOP2000, Signal Processing, Switzerland) to measure locally the
velocity and the shear stress distribution across the gap simultaneously. Three rotational
speeds of 2, 8 and 16 rpm were applied to assure the consistency of the data for all fibre
suspensions of various mass concentrations. A Herschel-Bulkley (HB) constitutive model
was used to fit the velocity profiles and to predict the measured steady-state flow curves
obtained by conventional rheometry.
3.3. Results and Discussion
3.3.1. Conventional rheometry analysis
After pre-shearing all suspensions at conditions summarized in Table 2-2,
different shear stress values were applied and the resulting steady-state shear rates were
obtained. The steady-state flow curves were then constructed using all data points
generated with this procedure. Figure 3-1 illustrates the results obtained for 2.5 wt.% pulp
suspensions.
57
Figure 3-1: Steady-state flow curves of several 2.5 wt.% pulp suspensions at 23
°C. Note
that there is no sign of yield stress over the range of shear rates used.
58
Pulp suspensions are highly shear-thinning fluids above the apparent yield stress.
By increasing the shear rate, fibre networks and fibre flocs rupture and the suspension
flows more readily. This causes the shear-thinning behaviour of pulp suspensions over a
wide range of shear rate, as can be seen from Figure 3-1b where the viscosity for all the
2.5 wt.% pulp suspensions is plotted as a function of the shear rate (essentially the data of
Figure 3-1a).
However, reaching a certain high shear stress, pulp suspensions exhibit a
Newtonian flow regime, which is referred to as the turbulent or fluidized regime
(Kerekes, 1983; Bennington et al., 1991; Hietaniemi and Gullichsen, 1996). At this
critical shear stress, pulp suspensions rupture at the edge of the vane resulting in a
dramatic change in the measured shear rate. This can be clearly observed as a gap in the
measured shear rate values in Figure 3-1a (γ& ≈10-50 s-1
) over which no measurements
can be made. Entering this regime, a pulp suspension is sheared strongly along the axial
and radial directions and individual fibres and different fibre flocs move separately in a
random manner, while fluidized in the suspension (Bennington et al., 1991; Hietaniemi
and Gullichsen, 1996; Chen, 1997). The shear stress at which pulp fibre suspensions
begin to fluidize is referred to as the critical shear stress for the onset of turbulence or
fluidization (Bennington et al., 1991; Chen, 1997). This critical shear stress, denoted by
σd, is an important operational parameter in the pulp and paper industry as pulp
suspensions are typically processed in the fluidized state to reduce the energy
consumptions and the associated investment costs (Chen, 1997).
The critical shear stress values are extracted from the steady-state flow curves as
the values at which Newtonian flow behaviour begins. These are listed in Table 3-1 and
plotted in Figure 3-2 as a function of fibre mass concentration.
The dependency of the critical shear stress values on fibre mass concentration has
been correlated using a power-law model (b
md aC=σ ). The resulting fitted constants are
listed as an insert in Figure 3-2. It should be noted that similar correlations were derived
for the apparent yield stress of these pulp suspensions, as described in chapter 2.
59
Table 3-1: Critical shear stress for the onset of turbulence or fluidization of pulp suspensions
σd (Pa)
Cm SBK HW TMP SGW
0.01 62 55 51 39
0.02 151 96 114 63
0.025 256 134 150 88
0.03 311 175 175 132
0.04 448 222 266 176
0.05 663 336 412 257
Figure 3-2: The critical shear stress values for the onset of turbulence or fluidization of
several pulp suspensions as a function of fibre mass concentration. Solid lines are power-
law fits with constants shown in the insert.
Pulp fibre suspensions exhibit yielding behaviour (Gullichsen and Harkonen,
1981; Bennington et al., 1990; Swerin et al., 1993; Wikström et al., 1998). However, the
steady-state flow curves obtained using a conventional rheometrical technique exhibit
apparent yield stress values which are significantly lower than those reported in chapter 2
and in some cases even show no sign of a yield stress, at least in the investigated range of
shear stress values. The reasons for such a rheological behaviour are discussed in the next
section where the local velocity profiles are obtained and used to study the rheology of
such materials.
60
3.3.2. Velocity profile measurements
In this section the measured steady-state flow curves from conventional
macroscopic rheological measurements (presented above) are compared with those
deduced from the coupled UDV-rheometry technique. As discussed above an ultrasonic
Doppler velocimeter was used to determine local velocity profiles of various pulp
suspensions in conjunction with torque measurements with the Haake R12 rotovisco
viscometer. A Herschel–Bulkley (HB) model (Eq. 3-1) was used along with Eqs. (2-5)
and (2-6) to calculate the velocity profile across the gap of the rheometer (Eq. 3-2).
n
y Kγσσ &+= (3-1)
r
dr
K
hrrru
n
R
r
yy
1
22)( ∫
−
Τ
=
σπ
(3-2)
where σy, K and n are HB parameters and R1 and Ry are the vane and the yielding radii
while R1 ≤ r ≤ Ry.
The integral expression of Eq. (3-2) was solved for all types of pulp suspensions
at all investigated rotational rates in order to determine the HB constants, σy, K and n. The
HB constants obtained from Eq. (3-2) were then used to describe the flow curves of pulp
suspensions obtained by the conventional rheometry. Figures 3-3a-3d illustrate typical
experimentally determined velocity profiles and their comparison with those determined
numerically by using Eq. (3-2), for 3 wt.% pulp suspensions at three different rotational
rates.
The velocity decreases across the gap, starting from a maximum at the vane tip
and falling to zero at a certain distance referred to as the yielding radius Ry (Figure 2-1).
The shear stress decreases in the gap according to Eq. (2-5). The suspension contained in
the region between the vane tips and the yielding radius is in flow, while the fluid beyond
this region remains stationary.
61
62
Figure 3-3: Velocity profiles across the gap for 3 wt.% suspensions of a) SBK, b) HW, c)
TMP, d) SGW fibres at 23°C and three rotational speeds, namely 2, 8 and 16 rpm. The
solid lines are fits of the Herschel-Bulkley model. Arrows in the insert indicate the
nominal wall velocity which at low rotational speeds is lower due to the wall slippage.
Error bars indicate the 95% confidence interval of the mean.
63
As referred to above, the solid lines in Figs. 3-3a-3d are the predictions of the HB
model, in fact Eq. (3-2). The overall agreement between the HB model calculations and
the experimentally measured velocity profiles is satisfactory. It is noted that the HB
model with the same constants adequately predicts the velocity profiles obtained at
different rotational rates.
Coupled UDV-rheometry technique revealed convincingly the yielding behavior
in pulp suspensions and the apparent yield stress values predicted by the HB model are in
agreement with those reported in chapter 2. Nevertheless, conventional rheometry is not
always capable of detecting yielding behavior. This is due to apparent wall slippage that
occurs at small rotational speeds as shown as an insert in Figs. 3-3a-3d, where the arrows
indicate the linear speed at the vane surface based on the nominal rotational speed. While
there is practically no apparent wall slippage (no difference between the nominal and
actual linear speeds) at higher rotational rates (8 and 16 rpm), all types of pulp
suspensions exhibit an apparent wall slip of around 20% at the lower vane rotational rate
of 2 rpm. This behavior was also previously observed for nonadhesive concentrated
emulsions (Bécu et al., 2006) and pastes of microgel particles (Meeker et al., 2004a).
In such cases, using local velocity measurement techniques to study the
rheological behavior of complex fluids has many advantages over the conventional
techniques. One of which is that the wall slip does not affect the experimental data. These
techniques measure the actual bulk shear rates and calculate the shear stress using the
basic momentum balance equations and the interpretation of the experimental data does
not depend on any wall artefacts (Bécu et al., 2006).
The UDV-rheometry technique was also used to measure the local velocity
profiles across the gap in the cup-and-vane geometry for pulp suspensions of different
fibre mass concentrations. Figures 3-4a-4d illustrate the obtained velocity profiles and the
calculations based on the HB model for all types of pulp suspensions.
64
65
Figure 3-4: Velocity profiles across the gap for, a) SBK, b) HW, c) TMP, d) SGW pulp
suspensions at 23°C, vane rotational rate of 16 rpm and several mass concentrations.
Solid lines are the best fits to the data by the Herschel-Bulkley model with constants
listed in the insert. Error bars indicate the 95% confidence interval of the mean.
66
Again, the HB model with the same constants accurately describes the
experimentally measured data for different vane rotational velocities (three in total).
However, as it was observed before in chapter 2, pulp suspensions at higher fibre
concentrations exhibit a discontinuous transition through the yielding radius. This
behaviour is studied in more detail in chapter 4. The resulting fitted HB constants are
summarized in Table 3-2a-2d for all the investigated pulp suspensions and fibre mass
concentrations.
The rheological behaviour of pulp suspensions depends on the physical properties of
the fibres. Fibres tend to form networks due to a number of attractive forces, including
colloidal, mechanical surface linkage, elastic fibre bending and surface tension, although
mechanical entanglement is the greatest (Kerekes et al. 1983). Fibre properties, such as
fibre length, flexibility and elastic modulus contribute to these forces and affect the
rheological behaviour of the suspension.
More flexible and longer fibres permit greater contact between adjacent fibres,
increasing mechanical linkages and therefore the apparent yield stress. Due to differences
in fibre length and flexibility, the apparent yield stress and the flow curves decreases
from SBK > TMP ≅ HW > SGW at a given mass concentration. Increasing suspension
concentration increases the number of fibre entanglements, the strength of the fibre
network formed and hence increases the apparent yield stress and the consistency index
(K) while decreases the shear-thinning index (n) in the HB model (Table 3-2).
67
Table 3-2: Herschel–Bulkley constants for a) SBK b) HW c) TMP and d) SGW pulp
suspensions as functions of the fibre mass concentration
a) SBK n
y Kγσσ &+=
σy K n
0.01 10±3 23±2 0.20±0.03
0.02 43±8 39±7.5 0.20±0.02
0.025 110±10 55±2.5 0.19±0.03
0.03 147±15 71±4.6 0.17±0.02
0.04 271±55 80±4.5 0.14±0.02
0.05 415±60 112±10 0.11±0.01
b) HW n
y Kγσσ &+=
σy K n
0.01 7±1 18±3 0.21±0.02
0.02 21±2 32±4.6 0.20±0.03
0.025 23±2 42±4.5 0.19±0.01
0.03 56±7 56±7.6 0.18±0.01
0.04 93±14 57±8 0.15±0.03
0.05 173±12 84±6 0.13±0.02
c) TMP n
y Kγσσ &+=
σy K n
0.01 9±2 18±1 0.21±0.02
0.02 18±6 29±2.5 0.2±0.01
0.025 21±3 44±3 0.21±0.01
0.03 54±14 52±6.5 0.19±0.02
0.04 132±14 57±5.3 0.17±0.01
0.05 251±24 76±5 0.13±0.03
d) SGW n
y Kγσσ &+=
σy K n
0.01 1±0.5 14±3.1 0.23±0.02
0.02 12±3 17±2.8 0.21±0.01
0.025 19±3 23±2.3 0.21±0.01
0.03 25±6 35±4.6 0.20±0.03
0.04 73±12 41±6.1 0.18±0.03
0.05 143±18 62±12 0.14±0.02
68
3.3.3. Comparison of the conventional rheometry and the UDV
techniques
Figures 3-5a-5d compare the HB model predictions where constants were
obtained from local velocity profile measurements (solid lines) with experimental data
obtained from conventional rheometry. The HB model agrees well with the
experimentally measured flow curves up to the onset of the turbulent regime. It should be
noted that the term “turbulent” used here and in many other pulp and paper scientific
journals should not be confused by the “turbulent” regime defined by the Re number (See
chapter 1). At shear stress values close to the apparent yield stress, the data obtained by
the conventional rheometry technique are all lower than those predicted by HB model and
those obtained by velocimetry technique. This is clearly due to wall slip.
69
70
Figure 3-5: Steady-state flow curves for, a) SBK, b) HW, c) TMP, d) SGW pulp
suspensions at 23°C and several mass concentrations. Solid lines are the predictions of the
Herschel-Bulkley model with constants obtained from the fits to the local velocity
profiles (see Figure 3-4). Note that there is a deviance from the Herschel-Bulkley model
at low shear rates due to wall slippage.
During the flow of suspensions, particles/fibres cannot efficiently attach to the
wall physically. This leads to the formation of a thin layer of fluid adjacent to the wall
referred to as the "apparent slip layer" which has been observed in different types of
suspensions and gels (Bramhall and Hutton, 1960; Vinogradov et al., 1975 and 1978;
Coussot et al., 1993; Jana et al., 1995; Cloitre, 2000; Bertola et al., 2003; Meeker et al.,
2004a,b; Kalyon, 2005). The influence of such a slip layer is more pronounced at low
shear rates and is reduced as the shear rate increases.
Pulp suspensions are composed of large fibre flocs which make it difficult for
them to sufficiently occupy the space adjacent to the vane. Therefore, a slip layer forms
around the vane. Increasing the shear rate, some fibre flocs rupture into smaller flocs and
into individual fibres. Fibres redistribute more evenly around the vane and thus wall
71
slippage is diminished since better contact between the vane and fibres is achieved. Due
to the presence of wall slippage and the fact that the flow curves obtained by
conventional rheometry technique are estimated from the wall velocity (arrows in the
insert of Figs. 3-3a-3d), conventional rheometry results a different shear rate from the
actual shear rate imposed to the fluid.
3.3.4. Effect of pH and lignin on the rheology of SBK and TMP
suspensions
Fibre volume concentration and physical properties of fibres significantly
influence the apparent yield stress of pulp fibre suspensions (Bennington et al., 1990).
More specifically, increasing the fibre elasticity and/or the fibre aspect ratio enhances the
fibre entanglement and the apparent yield stress of suspensions according to Eq. (1-7).
Coupled UDV-rheometry technique was used to obtain the velocity profiles of 1,
3 and 5 wt.% suspensions of SBK (without lignin) and TMP of the same fibre mass
concentrations (with lignin) at vane rotational rates of 8 and 16 rpm. To examine the
effect of pH, suspensions were prepared at fixed pH values ranging from 4-10 covering
both acidic and alkaline regions. A Herschel-Bulkley rheological model was used to fit
the obtained velocity profiles and the rheological parameters were then obtained as
illustrated in Figures 3-6a,b and 3-7a,b for SBK and TMP suspensions respectively.
Generally, no significant change was observed in the rheological behaviour of
suspensions over the acidic region. However, entering the alkaline region, the apparent
yield stress σy and the HB consistency index K increased as a function of pH (see Figures
3-6a,b and 3-7a,b).
72
Figure 3-6: Velocity profiles across the gap for SBK at vane rotational rate of 16 rpm at
a) 1 wt.%, b) 3 wt.%, pulp suspensions at 23°C and pH=4,6, 8 and 10. Solid lines are the
best fits to the data by the Herschel-Bulkley model with constants listed in the insert.
Error bars indicate the 95% confidence interval of the mean.
73
This behaviour is due to two reasons. First, as pH increases over the alkaline
region, fibres swell and more flexible fibres are produced. The increased fibre flexibility
promotes conformability, thus allowing the fibres to form more fibre-fibre contacts and to
achieve stronger fibre networks (Toven, 2000). This in turn increases the suspension
apparent yield stress and the HB consistency index. Second, the swollen fibres occupy a
larger volume in the suspension; this results in higher fibre volume concentrations Cv
hence increase the suspension apparent yield stress according to Eq. (1-7).
The percentage increase in the apparent yield stress σy and consistency index K of
pulp suspensions at pH=6, 8 and 10 compared with those at pH=4 has been summarized
in Table 3-3 for SBK and TMP suspensions. The dependency of the apparent yield stress
on the pH of the suspension is more pronounced at lower fibre mass concentrations. This
is due to the availability of more space between individual fibres which facilitates the
fibre swelling process.
Pulp suspensions exhibit a considerable change in the rheological properties when
pH increases from 6 to 8. However, further increase in pH from 8 to 10 does not affect
the rheological properties significantly. This is probably due to the fact that fibres can
only swell up to a maximum level regardless of the pH.
74
Figure 3-7: Velocity profiles across the gap for TMP at vane rotational rate of 16 rpm at
a) 1 wt.%, b) 3 wt.%, pulp suspensions at 23°C and pH=6, 8 and 10. Solid lines are the
best fits to the data by the Herschel-Bulkley model with constants listed in the insert.
Table 3-3: Percentage increase of the apparent yield stress and consistency index of a) SBK
and b) TMP pulp suspensions compared with those at pH=4
a) SBK % increase compared with pH=4
pH=6 pH=8 pH=10
σy K σy K σy K
0.01 11 9.5 111 48 177 62
0.03 3.5 3 30 25 48 47
0.05 3.75 3.7 26.5 21 32 34
b) TMP % increase compared with pH=4
pH=6 pH=8 pH=10
σy K σy K σy K
0.01 12.5 20 75 46 125 66
0.03 8 6 34 27 46 41
0.05 4.8 5 75 7.5 86 19
Wood fibre is composed of various constituents one of which is lignin. Lignin is
an amorphous, highly branched, three dimensional phenolic polymer, which lends rigidity
and cohesiveness to the wood tissue (Biermann, 1996). Lignin serves as a glue to keep
75
fibres together in the wood matrix and maintains the rigidity of fibres. Due to these
functions lignin removal enhances fibre swelling (Stone et al., 1968; Ahlgren, 1970;
Lindstrom et al., 1980; Westman et al., 1981; Ehrnrooth, 1982). As seen in Table 3-3, the
percentage increase in the apparent yield stress and the HB consistency index of TMP
pulp suspensions are lower than those of SBK pulp suspensions at the same pH values.
This is clearly due to the higher lignin content of the TMP fibres which makes them less
susceptible to swelling.
These observations explain the importance of studying the rheological properties
of pulp fibre suspensions under controlled experimental conditions. Differences in the
suspension pH values and pulp fibre properties lead to different final rheological
properties.
3.4. Summary
The rheological properties of pulp fibre suspensions using conventional rheometry
and an ultrasonic Doppler velocimetry technique were studied. Increasing the fibre mass
concentration, pulp suspensions were found to exhibit higher apparent yield stress and
shear-thinning behaviour. More specifically, increasing the fibre mass concentration, the
apparent yield stress and the consistency index in the HB model (K) were found to
increase, while the power-law index in the HB model (n) was found to decrease.
Pulp suspensions were found to exhibit a Newtonian behaviour beyond a certain
shear stress. The critical shear stress values required to begin the Newtonian regime were
measured for several pulp fibre suspensions. The critical shear stress was found to depend
on fibre mass concentration following a power-law dependence with exponents in the
range of 1.1 to 1.47.
Data obtained by using conventional rheometry techniques (macroscopic
measurements) suffer from wall artefacts despite the use of a vane in large cup geometry
that is known to minimize wall slippage. Velocity profile measurements through the use
of an ultrasonic Doppler velocimetry technique on the other hand, uniquely identify the
real velocity distribution and yielding radius in the gap. This technique measures the
actual bulk shear rate imposed on the fluid and calculates the shear stress using the basic
76
momentum balance equations, thus eliminating wall slip effects. Hence, this technique
gives an accurate determination of the flow curves of complex fluids such as pulp
suspensions. The velocity profile determination technique is useful to study other types of
complex fluids such as biomass slurries and other types of fibre suspensions the rheology
of which is not simple to be studied by conventional rheometry.
Apparent yield stress and HB consistency index were found to increase as pH
increased over the alkaline region in both SBK and TMP pulp suspensions. This
behaviour is attributed to the increase in the flexibility of pulp fibres as pH increases. The
more flexible fibres make stronger fibre networks and produce higher fibre volume
concentrations hence increase the apparent yield stress. Fibres with less lignin content are
more susceptible to swelling, and as a result the rheological properties of fibre
suspensions with less lignin content, exhibit stronger dependency on the suspension pH.
77
4. Thixotropy, Yielding and Ultrasonic Doppler
Velocimetry in Pulp Fibre Suspensions4
4.1. Introduction
Thixotropy is the decrease of viscosity with time when a sample is sheared from
rest and its subsequent recovery when flow stops (Schalek and Szegvari, 1923; Mewis
and Wagner, 2009). Extensive studies of thixotropy have taken place and been reported in
the scientific literature for various systems. Some noteworthy publications include the
reviews of the field by Mewis (1979), Barnes (1997), and Mewis and Wagner (2009).
Due to the presence of microstructure within the sample, thixotropic materials
often exhibit an apparent yield stress i.e. a minimum shear stress is required to rupture the
structures and to initiate flow (Mewis and Wagner, 2009; Ovarlez et al., 2009). In other
words, unless the apparent yield stress is exceeded, flow does not take place. In an ideal
yield-stress fluid, the shear rate is constant or exhibits a continuous spatial profile and
models such as Herschel-Bulkley, Casson or Bingham precisely predict the velocity
profiles in a given geometry (Bonn and Denn, 2009).
However, most of the concentrated suspensions do not conform to this definition
of apparent yield stress (Raynaud et al., 2002; Bonn et al., 2002; Baudez et al., 2004;
Jarny et al., 2005). The presence of thixotropy and yielding is often associated with shear-
banding. In this case, the shear rate profile exhibits an apparent discontinuity, i.e., the
shear rate takes two significantly different values for the same shear stress (Coussot et al.,
1993; Mas and Magnin, 1994; Pignon et al., 1996; Ovarlez, 2006). This can also be
viewed as a pseudo phase separation, where the flowing complex fluid is spatially split
into two regions bearing the same shear stress, one being the low-shear-rate and the other
the high-shear-rate region. This is the banding instability that gives rise to a
4 A version of this chapter has been published. Derakhshandeh, B., Vlassopoulos, D., Hatzikiriakos, S.G.,
2011. Thixotropy, yielding and ultrasonic Doppler velocimetry in pulp fibre suspensions. Rheologica Acta
doi:10.1007/s00397-011-0577-7.
78
discontinuous velocity profile (Olmsted, 2008; Dhont and Briels, 2008). Typically, this
translates into a stress plateau region in the flow curve (Coussot et al., 1993). However,
the inverse is not always true, i.e. the appearance of stress plateau in the flow curve does
not necessarily mean that there is shear banding (Meeker et al., 2004a,b). Note also that
often a thin slip layer is observed with slip velocities being a weak (power-law) function
of the shear stress and it is unclear if banding occurs or not (Becu et al., 2006; Erwin et
al., 2010; Coussot and Ovarlez, 2010). Wormlike micelles represent the most extensively
studied and best understood shear-banding experimental system, which exhibits a strong
shear thinning but typically no yield stress (Cates and Fielding, 2009). From the above it
is evident that the field is very rich and there are different macroscopic reflections of
shear banding, although the origin always appears to be the coupling of the system’s
order parameter to the flow field. A further remark is that there is often a distinction made
between shear banding and shear stress localization. Whereas both reflect discontinuous
velocity and discontinuous shear rate, the former is associated with the steady thinning
flow curve and finite velocities in the two bands; on the other hand, the latter is the
pseudo phase separation situation with a nearly zero or unsteady velocity branch and a
finite velocity branch (Coussot, 2007). For the present purposes we shall call the velocity
discontinuity banding, but note that it reflects coexistence behaviour.
Concentrated suspensions and pastes such as paint, mud and cement are known to
be yielding and often thixotropic materials (Barnes, 1997; Raynaud et al., 2002). Shear-
banding is often observed in these systems and, given the complex flow behaviour, a
number of studies have been devoted to develop appropriate techniques to study their
rheology. It is now well-known that velocimetry techniques such as magnetic resonance
imaging (MRI), particle image velocimetry (PIV) and ultrasonic Doppler velocimetry
(UDV) can be successfully implemented to study thixotropic systems (Raynaud et al.,
2002), and shear-banding (Mas and Magnin, 1994; Callaghan, 2008; Manneville, 2008).
Generally, models such as Herschel-Bulkley (HB) have been used to represent the
flow behaviour of pulp fibre suspensions at different fibre mass concentrations
(Pettersson, 2004; Ventura et al., 2007). Chapter 3 of this thesis also indicates that the HB
model adequately describes the velocity profiles and the flow behaviour of pulp
suspensions. However, in some cases at higher fibre mass concentrations, the obtained
79
velocity profiles exhibited a discontinuous change in the slope at the interface between
the yielded and un-yielded regions. This is typical behaviour of materials which exhibit
shear banding (Olmsted, 2008).
As discussed in the previous chapters, pulp suspensions are heterogeneous
systems containing millimetre-sized fibres and centimetre-sized fibre flocs. The
discontinuity in the velocity profiles at the transition from the yielded to the un-yielded
zone can also be due to the presence of large moving flocs in the layer next to the un-
yielded region. In this case, UDV probes finite velocities for the moving fibre flocs and
drops to zero in the next layer. Therefore, at this point it is not clear, whether pulp
suspensions display shear banding as they go through yielding transition.
The literature review presented in chapter 1 indicates that past works have
generally focused on the apparent yield stress measurement, post-yield flow behaviour
and some particular aspects of pulping or papermaking. One aspect that has not been
addressed to date is measurement and analysis of thixotropy and possible shear-banding
effects in pulp suspensions, particularly the more concentrated ones.
This chapter addresses the time-dependent rheology of concentrated pulp
suspensions with emphasis on thixotropy, viscosity bifurcation and shear-banding.
Ultrasonic Doppler velocimetry (UDV) is used to explore the velocity profiles across the
gap of a vane in large cup geometry in order to study the yielding transition in pulp
suspensions. The velocity profiles are then used to propose a model to describe the
behaviour of pulp sheared in the yielded region. In this chapter, we study a 6 wt.% pulp
fibre suspension higher than those used in the previous chapters since the phenomena of
thixotropy and shear banding are more dominant at high mass concentrations.
4.2. Materials and Experimental Testing
Pulp fibre suspensions of 6 wt.% were prepared from stone-ground wood (SGW;
Paprican, Pointe-Claire, QC) using the procedure explained in section 2.3 of chapter 2.
The pulp fibre properties are also summarized in Table 2-1. Having shortest fibres and
80
least extent of flocculation amongst commercially available pulp fibres, SGW pulp
suspension is an ideal candidate for this study.
A stress-controlled Kinexus rotational rheometer (Malvern instruments Ltd, UK)
was used to perform all the rheological experiments with a vane in large cup geometry
similar to that described in chapter 2. As we make use of a wide gap Couette geometry,
different sets of torque-rotation velocity are required to calculate the shear rate within the
gap using Eq. (4-1) (Coussot, 2005):
t
t
Τ∂
Ω∂Τ= 2),( 1σγ& (4-1)
where Τ is the applied torque on the vane corresponding to shear stress σ1 and Ω is the
vane rotational velocity at time t.
We are limited to such a more complicated approach as simpler common
geometries such as parallel-plate and cone-plate geometries fail when used to study pulp
suspensions as discussed before. Rheological experiments include hysteresis loops,
apparent flow curves by applying shear stress ramps, transient experiments by changing
the shear stress in a stepwise manner and creep experiments.
In order to measure the local velocities within the suspension, a rate-controlled
Haake RV12 viscometer equipped with a vane geometry (see details in section 2.2 of
chapter 2) was coupled with a pulsed ultrasonic Doppler velocimeter (Model DOP2000,
Signal Processing, Switzerland). As discussed in chapter 3 at low rotational rates of less
than 2 rpm wall slippage occurs at the tip of the vane. On the other hand, at high
rotational rates the pulp becomes fully fluidized, and it becomes difficult to obtain
accurate velocities as the data become noisy. Therefore, to prevent these two effects, vane
rotational speeds of 8, 16 and 32 rpm were selected to examine the behaviour of the
samples. These were found to be appropriate rates based on the signals obtained from
UDV and the rheological response of pulp suspensions. Applying these rotational rates,
the velocity profiles were measured at both steady-state and transient conditions.
81
4.3. Results and Discussion
4.3.1. Hysteresis loops
A typical experiment to study thixotropy is the measurement of the hysteresis
loop. In this measurement, the shear stress or shear rate is increased and then decreased
continuously or in small steps. A thixotropic material exhibits a hysteresis loop as shown
in Figure 4-1 for a 6 wt.% pulp fibre suspension. In the hysteresis experiment, the flow
time induced by the rheometer should be shorter than that required for structure build-up
(Beris et al., 2008; Coussot and Ovarlez, 2010). In our measurement, the shear stress was
increased linearly from 50 Pa to 350 Pa with a ramp rate of 1 Pa/s to ensure flow times
shorter than the time required to build-up structures within the sample. This will be
confirmed later by the results obtained from transient experiments.
Figure 4-1: Hysteresis loop for 6 wt.% pulp fibre suspension. Sample was pre-sheared at
350 Pa for 2 minutes followed by 20 minutes rest. Shear stress increased from 50-350 Pa
in 300 s and decreased over the same time frame. The arrow indicates the plateau in the
flow curve from 6 to about 18 s-1
.
82
A limitation of hysteresis experiment is that it is not possible to differentiate the
effects of time and shear rate as both contribute in the experimental testing (Bird and
Marsh, 1968; Mewis and Wagner, 2009). Therefore, other characterization tools are
required to confirm thixotropy. Nevertheless, there are two interesting observations in the
hysteresis loop of pulp suspension plotted in Figure 4-1. First, at a shear stress of ~278 Pa
the shear rate jumps from about 6 to about 18 s-1
generating a plateau in the flow curve
(the arrow in Figure 4-1). The presence of a plateau in the flow curve is known to be due
to either wall slip (Hatzikiriakos and Dealy, 1992) or shear-banding (Coussot, 2005;
Olmsted, 2008), an effect which has also been observed in many pasty materials (Coussot
et al. 1993, 2010). This is examined in more detail later.
Secondly, based on the shape of the hysteresis loop (Figure 4-1) at low shear rates
it can be concluded that low shear rates induce structure formation within the pulp
suspension (Kanai and Amari, 1995). The hypothesis is that at lower shear rates the
deformation is not large enough to either break-down or align the fiber domains. Instead,
smaller fibre flocs merge to make structures (domains) of larger dimensions and
individual fibres collide to make and/or be incorporated into the fibre flocs. In contrast, at
high shear rates the upward and downward flow curves overlap as pulp adopts the same
state of structures.
Next, the effect of rest time (before measurement) on the rheological behaviour of
pulp suspension is investigated. In the field of glassy suspensions (a particular, much-
studied class of structured systems) this time is called waiting time. Samples were pre-
sheared with a shear stress of 350 Pa for 2 minutes and then left to rest for different time
periods of 2, 5, 10 and 20 minutes prior to be subjected to a shear stress ramp to obtain
the flow curves. It should be noted that the pre-shearing stress of 350 Pa is in the thinning
regime (Figure 4-1) where the sample is fully fluidized to ensure rupturing of the
structures within the sample. In the case of pulp fibre suspensions, it is not feasible to
estimate the relaxation times by means of linear viscoelasticity studies due to the
limitations associated with sample loading into the rheometer as discussed above.
Nevertheless, it is suggestive that relaxation times are ultra-long, as expected in pasty
materials and suspensions (Coussot et al., 2005). Therefore, to appropriately select
different rest times, the first two time periods (2 and 5 min) were selected close to each
83
other to check reproducibility of the time effects, while the other two time periods were
chosen to be further apart to provide more information on the time-dependent rheology of
pulp taking into account proper experimental conditions (e.g. not too long in order to
avoid evaporation problems).
The results (various flow curves corresponding to various rest times) are plotted
in Figure 4-2. As the rest time increases, the flow curves shift upward, i.e. the viscosity
increases with rest time, presumably reflecting structure build-up. Pre-shearing the
suspension ruptures the structures within the sample and makes the fibres to orient.
However, left at rest for sufficient period of time, fibres settle, but given their vast
polydispersity, they form a 3D network which is swollen with water throughout the
sample. In this case, the sample should be very shear-thinning as shown in chapter 3. This
also explains the increase in the viscosity of the suspension with rest time. Here again,
there exists a plateau in the flow curves of pulp suspension the level of which strongly
depends on the shear history and particularly on the rest time prior to the measurement.
Moreover, flow curves overlap at high shear rates as the fibre structures in the suspension
are ruptured and/or aligned, at least partially, to the same extent.
Figure 4-2: Apparent flow curves of pulp fibre suspension. Samples were pre-sheared at
350 Pa for 2 minutes followed by 2, 5, 10 and 20 minutes rest. The arrow indicates the
plateau in the flow curve.
84
4.3.2. Transient behaviour during shear flow
To independently study the effect of time and shear history on the behaviour of
pulp suspension, a preferred experiment is to apply step changes in the shear stress/shear
rate and measure the transient change of the shear rate/shear stress until a steady-state is
reached. Therefore, here in contrast to the hysteresis loop technique, the relative effects
of time and shear can be easily decoupled and resolved. This is typical of the approach
followed in thixotropic suspensions (Erwin et al., 2010).
4.3.2.1. Build-Up Behaviour
Pulp suspension was first sheared at initial shear stress values of σi=350 and 370
Pa (both in the thinning regime of Figure 4-1) until steady-state shear rates were
achieved. This ensures the well-defined initial state of the sample prior to any further
experimental testing. To study the kinetics of structural growth during shear, shear stress
was then suddenly reduced to σe=280, 285, 290 and 300 Pa and the evolution of viscosity
with time was followed as shown in Figures 4-3a and 4-3b for σe=280 and 300 Pa
respectively. During the decrease of the shear stress from σi to σe, the viscosity increased
to a new steady-state as microstructures evolved in the suspension. It should be noted that
a pulp suspension, regardless of the magnitude of the initial applied shear stress σi, adopts
the same final steady state viscosity (Figure 4-3a and 4-3b). This clearly shows the
reversibility of the process, an essential element of thixotropy. These observations
indicate that the pulp fibre suspension is a thixotropic material. It is presumed that
increasing the fibre concentration, fibre size and flexibility increase the extent of
thixotropy in pulp suspension, although these have not been examined here.
In such a flocculated system, the final equilibrium state is governed by a number
of parameters which facilitate structuring and/or destructuring. These parameters are in
principle of two kinds: hydrodynamic shear stresses which pull the structures apart, but
also occasionally collide them, and Brownian motions (Mewis and Wagner, 2009). These
parameters are often incorporated into the constitutive equations to model thixotropy by
means of a variable structure parameter. The variable structure parameter depends on the
85
actual state of the structure, evolves with the flow history and is often described with the
help of a kinetic equation (Coussot, 2007, and references therein).
Figure 4-3: Structure build-up in pulp suspensions from initial shear stresses of σi=350
and 370 Pa to (a) Sudden decrease of the shear stress to σe=280 Pa (b) σe=300 Pa. Solid
lines show the fits of a KWW function.
86
The contribution of the Brownian motions relative to the hydrodynamic forces in
a dilute system can be expressed by the Peclet number:
rDPe
γ&= (4-2)
where Dr is the rotary diffusion coefficient for a fibre given (Macosko, 1994) by:
38
5.02ln3
l
d
lTk
Ds
B
rπη
−
= (4-3)
where Bk is the Boltztmann constant, T is the absolute temperature, ηs is the medium
viscosity, l and d are the fibre length and diameter respectively. We have calculated this
number for the pulp suspension to evaluate the extent of the Brownian motions although
the pulp suspension used in this study is a concentrated system. The contribution of the
Brownian motions to structure build-up in pulp is negligible as Pe number will be in the
order of 109 for the smallest particles i.e. l=0.07 mm (Table 2-1). Therefore, the transient
response of pulp suspension to a sudden change in the shear stress is expected to be
mainly governed by the strain-induced rearrangements. This will be studied in more
detail as we try to quantify the transient behaviour.
In order to quantify thixotropy, the transient response of the sample (Figures 4-3a
and 4-3b) was fitted to a stretched exponential or Kohlrausch-Williams-Watts (KWW)
function (Eq. 4-4):
0 0( ) 1
t
e
β
τη η η η
−
∞
= + − −
(4-4)
where η0 and η∞ are the suspension viscosity prior and after shearing while τ and β (often
assumed to be equal to 1) are constants (Barnes, 1997).
The KWW function was found to adequately describe the structural growth of
pulp suspension during shear as shown by the solid lines in Figures 4-3a and 4-3b. The
corresponding characteristic times (τ) obtained from Eq. (4-4) are summarized in Table 4-
1 for samples at different initial and final flow conditions.
87
Table 4-1: Thixotropic time constants for build-up
Build-up
Initial shear stress, σi=350 (Pa) Initial shear stress, σi=370 (Pa)
Final shear stress,
σe (Pa)
Thixotropic time
constant, τ (s)
Final shear
stress, σe (Pa)
Thixotropic time
constant, τ (s)
280 21.6 280 28.8
285 19.8 285 23.7
290 12.0 290 17.4
300 5.8 300 11.4
In samples sheared at the same initial shear stress, σi, the corresponding
characteristic time (τ) decreases linearly as the final shear stress σe increases. This again
indicates that the structure build-up in pulp suspension is governed by shear-induced
collisions. The same dependency between the characteristic times and the magnitudes of
the final shear stress was observed before for bentonite dispersions (Mylius and Reher,
1972), thixotropic fumed silica dispersions (Dullaert and Mewis, 2005) and layered-
silicate montmorillonite suspensions (Mobuchon et al., 2007). It should be noted that the
stretching exponent β in Eq. (4-4) was independent of the flow history and remained
constant close to 1 for all measurements. In other words the structure build-up in pulp
fibre suspensions is a single exponential process and can be characterized by one
characteristic time. This indicates that pulp fibre flocs have a narrow size distribution in
the suspension.
Figures 4-3a, 4-3b and Table 4-1 show that pulps which were initially sheared at a
lower shear stress of σi=350 Pa evolve faster with shorter characteristic times compared
with those sheared at σi=370 Pa. Suspensions pre-sheared at lower shear stress include
more developed structures and thus respond faster during the structure growth process.
Next we study the structure breakdown in pulp suspensions.
4.3.2.2. Structure Breakdown
A similar procedure as above was followed to study the flow induced breakdown
of structures in pulp suspensions. Samples were pre-sheared at two different initial shear
stress values of σi=100 and 200 Pa until a steady-state shear rate was achieved. Shear
88
stress was then suddenly increased to σe=280, 300, 320 and 350 Pa and the transient
change in the viscosity with time was followed.
Figure 4-4 reports the transient change in pulp viscosity for jumps from σi=100 Pa
to different final shear stress values. Here again the same empirical KWW functions of
Eq. (4-4) were fitted to the data (solid lines in Figure 4-4) with constants given in Table
4-2. This model adequately describes the kinetics of the structure breakdown with
stretching exponents of close to 1.
Figure 4-4: Structure breakdown in pulp suspensions from an initial shear stress of
σi=100 Pa to 280, 300, 320 and 350 Pa. Solid lines show the fits of a KWW function.
Generally, the characteristic times obtained for the structure breakdown are
shorter than those of structure build-up. Furthermore, the characteristic times obtained for
the structure breakdown exhibit less dependency on the initial shear history. This
indicates that the structure breakdown is mostly governed by the magnitude of the final
applied shear stress, and that shear history does not play a major role in the structure
breakdown process.
89
Table 4-2: Thixotropic time constants for breakdown
Breakdown
Initial shear stress, σi=100 (Pa) Initial shear stress, σi=200 (Pa)
Final shear stress,
σe (Pa)
Thixotropic time
constant, τ (s)
Final shear
stress, σe (Pa)
Thixotropic time
constant, τ (s)
280 9.8 280 9.4
300 7.1 300 6.9
320 5.9 320 6.1
350 3.8 350 3.5
4.3.3. Viscosity bifurcation
To study in greater detail the flow of suspension over the observed plateau in the
flow curves plotted in Figures 4-1 and 4-2, and associated yielding behaviour, creep
experiments were performed at various shear stress values over sufficiently long times.
The samples were pre-sheared prior to the experiments at a shear stress of 350 Pa for 2
minutes then left to rest for 20 minutes before further testing.
A range of shear stress values was applied and the shear rate was measured with
time as depicted in Figure 4-5a. At shear stresses above a critical value ( 279≅cσ Pa), the
shear rate increases rapidly to a steady-state value indicating flow. However, below this
critical shear stress, which corresponds to a critical shear rate, cγ& , the shear rate decreases
with time until ultimately flow stops. This corresponds to a discontinuous shear rate
profile as will be shown in the next section by the local measurement of the velocity
profile across the gap of the rheometer. In other words, there is no stable flow below a
critical shear rate, an effect referred to as viscosity bifurcation, as shown in Figure 4-5b,
where the viscosity is plotted as a function of time. This has been proposed as an absolute
measure of apparent yield stress (Da Cruz et al., 2002; Coussot et al., 2002b). It should be
noted that it is difficult to measure the very exact value of the critical shear stress in pulp,
although it was found to be in the range of 278 280c
σ ≅ − Pa.
In an “ideal” yield stress fluid, as discussed before, flow stops at 0=cγ& .
However, this is not the case for the concentrated pulp suspension studied here neither for
many pasty materials due to continuous internal rearrangements and local stresses
(Coussot et al., 2002c; Bertola et al., 2003; Jarny et al., 2005).
90
Figure 4-5: (a) Creep tests and (b) the change in viscosity in time showing viscosity
bifurcation. Pulp suspensions were pre-sheared at 350 Pa for 2 minutes followed by rest
for 20 minutes.
91
In the next section, the ultrasonic Doppler velocimeter is used in conjunction with
a rate-controlled rheometer to investigate thixotropy and possible shear banding and to
study the transient flow of pulp suspensions.
4.3.4. Local velocity profiles
The discontinuity of the shear rate profile discussed above would be more clearly
shown by local velocity measurements. Figure 4-6 depicts the steady-state velocity
profile obtained at a vane rotational rate of 16 rpm which corresponds to a nominal shear
rate of ~20 s-1
. Velocity is at maximum at the tip of the vane (r=12.5 mm) and decreases
across the gap until the flow stops at a radius referred to as the yielding radius (Ry).
We then measured the velocity profile across the gap of the rheometer and solved
a Herschel-Bulkley model (Eq. 2-9) using the “least squares” method to find the best fits
of the HB model to the data as shown in Figure (4-6). The best fit of the HB model to the
velocity profile was obtained by constants of σ0=261 Pa, K=71 and n=0.2 as shown as
solid line in Figure (4-6). The measured velocity profile exhibits a discontinuous
transition from yielded to the un-yielded region (see Figure 2-2) and the prediction of a
Herschel-Bulkley model does not quite agree with the experimentally obtained velocity
profiles (Figure 4-6). In an ideal yield stress fluid the velocity profile progressively
decreases from a maximum at the vane to zero at the yielding radius. However, as
observed from Figure 4-6, the HB models (with different parameters) do not completely
predict the transition through yielding radius. This is due to the discontinuous change in
the slope of the velocity profile which is incompatible with predictions of velocity profile
by means of a HB model. The discontinuity in the velocity profile may come from two
possible sources, shear-banding and/or slippage. It should be noted that the HB model
was previously found to adequately predict the velocity profiles of pulp fibre suspensions
at lower fibre concentrations as discussed in chapter 3.
Pulp is a suspension of fibres and fibre flocs in water. Water is a low viscousity
fluid and thus fibres and fibre flocs are able to move easily in the suspension given
enough spatial freedom. Therefore, in the very last layer of the suspension in the yielded
region, fibres and flocs might slip over the ones in the first layer of the un-yielded region
92
and this might lead to such a discontinuity in the velocity profiles. Furthermore, a layer of
water may also be formed in the transition from yielded to the un-yielded region which in
turn can develop such discontinuous velocity profiles. Nevertheless, regardless of the
origin of such behaviour, pulp suspension at this concentration cannot be modeled as an
ideal yield stress fluid as all models describing apparent yield stress predict a continuous
change of the velocity through yielding radius.
Figure 4-6: Steady-state velocity profile of pulp suspension at a vane rotational rate of 16
rpm. Pulp was pre-sheared at 350 Pa for 2 minutes with no time of rest after. Solid line is
the best fit by a Herschel-Bulkley model. Error bars indicate the 95% confidence interval
of the mean. Note that the HB model fails to predict the velocity profile due to the
discontinuous change in the slope of velocity profile through yielding.
As discussed above, the rest time prior to the experimental testing affects its
rheology. It is worthwhile to examine the corresponding changes in the velocity profiles
of the suspension as well. Pulp was pre-sheared at 350 Pa for 2 minutes and left at rest for
various time periods prior to the measurement of the velocity profiles, i.e. similar
experiments with those plotted in Figure 4-2. A vane rotational rate of 16 rpm was
suddenly applied and the variation of torque with time was followed using the rheometer.
While steady-state toque was attained, the velocity profile measurement was commenced
93
and 15 profiles were averaged. Figure 4-7 depicts the steady-state velocity profiles in the
suspensions left at rest for 0, 60 and 120 minutes. As implied from Figure 4-7 the un-
yielded region (or zero velocity) increased with the time of rest. This is more clearly
shown in Figure 4-8 where the yielding radius (Ry) decreases with the time of rest to a
constant final value.
Figure 4-7: Steady-state velocity profiles of pulp suspension at a vane rotational rate of
16 rpm. Pulp was pre-sheared at 350 Pa for 2 minutes and left at rest for 0, 60 and 120
minutes prior to the velocity measurement. Solid lines are eye-guiding lines.
The yielding radius, Ry, can be used to estimate the critical shear stress, σc, or, in
the case of an ideal yield stress fluid the apparent yield stress using Eq. (4-5):
22 y
cRhπ
σΤ
= (4-5)
where T is the steady-state torque from the rheometer and h is the height of the vane. The
critical shear stress values obtained from the steady-state velocity profiles are plotted
against the time of rest inside Figure 4-8.
94
Figure 4-8: Yielding radius as a function of the rest time deduced from the steady-state
velocity profiles. There is no significant change in yielding radius after ~100 min. Inset:
evolution of the critical shear stress with time of rest.
The critical shear stress of the pulp rested for 20 minutes was found to be ~275
Pa, which is in agreement with that of Figure 4-1 obtained by rheometry. Figure 4-8
indicates that the critical shear stress required to initiate a stable flow in the suspension
increases with the time of rest. This again reflects the time-dependency of the rheology of
pulp suspension.
Next, the evolution of the velocity profiles is studied during a transient test. Pulp
was pre-sheared at 350 Pa for 2 minutes followed by a 5 minutes rest time. The vane was
then suddenly fixed to rotate at 16 rpm and the velocity profiles were measured every 5
seconds until steady-state was achieved. Figure 4-9 illustrates the temporal change in the
velocity profiles of the suspension.
As the yielding radius increases with time, the velocity profiles become less
abrupt although they all exhibit the discontinuous change of the velocity in transition to
the un-yielded region. The yielding radius increases nearly exponentially with time until
95
steady-state is achieved as shown inside Figure 4-9. This functionality has been observed
before in pasty materials (Raynaud et al., 2002).
The velocity profiles obtained by the above procedures can be used to propose a
rheological model to describe the flow of pulp in the yielded region of the rheometer.
This will be discussed in the next section.
Figure 4-9: Transient velocity profiles of pulp suspension when the vane rotational rate
was suddenly increased to 16 rpm. Pulp was pre-sheared at 350 Pa for 2 minutes and left
at rest for 5 minutes prior to the velocity measurement. Solid lines are the eye-guiding
lines. Inset: The evolution of the yielding radius with time fitted to an exponential
function.
4.3.5. Rheological interpretation of the velocity profiles
As discussed before, in the case of concentrated pulp suspensions, there is a
critical shear stress σc which defines a limit between no-shear and significant shear. This
critical shear stress which is given by Eq. (4-5) remains constant at different velocities as
long as pulps experience the same shear history.
96
Coussot (2005) has suggested that the steady-state velocity profiles obtained at
different vane rotational rates to be analyzed together. This makes it possible to assess the
rheological behaviour of the sample over a wide range of shear rates. To do so, the
velocity profiles should be scaled with a velocity or distance to construct a master curve.
Here we adopt the same concept and scale the obtained velocity profiles with the yielding
radius Ry. Figure 4-10 reports the steady-state velocity profiles obtained at vane rotational
rates of 8, 16 and 32 rpm.
Figure 4-10: Steady-state velocity profiles at vane rotational rates of 8, 16 and 32 rpm.
Solid lines are eye-guiding lines. Note that no slippage was found at the tip of the vane.
Scaling the local radius within the gap of the Couette geometry by the yielding
radius Ry gives:
yR
rR = (4-6)
The local velocity at the dimensionless radius R then becomes:
yR
uU = (4-7)
97
where u (mm/s) is the local velocity across the gap and U is the scaled velocity (s-1
).
Accordingly, the shear rate and the shear stress distributions across the gap of the Couette
geometry become:
( )R
RU
RR∂
∂=)(γ& (4-8)
)()(2
2
RRr
Rr cy
c σσ
σσ ==
= (4-9)
Figure 4-11 depicts the velocity profiles measured at vane rotational rates of 8, 16
and 32 rpm, all falling along a single master curve quite well. Once a master curve is
obtained for the velocity profiles, various models can be fitted to the data to calculate the
shear rate distribution by using Eq. (4-8).
It should be noted that for a single material the shear rate distribution should be
the same regardless of the type of the model fitted to the master curve. Here, we fit a
model of the form Eq. (4-10) (solid lines in Figure 4-11) which was previously used
successfully for bentonite suspensions by Raynaud et al. (2002).
( )RRRU m −= −α)( (4-10)
Using Eqs. (4-8) and (4-10), the shear rate distribution across the gap becomes:
)1()1( +−+= mRmαγ& (4-11)
where α and m are constants. The constitutive equation in steady-state for pulp
suspension in the yielded region can then be derived by using Eqs. (4-8), (4-9) and (4-
11):
1
2
+= mAγσ & (4-12)
and
[ ]1
2
)1(+
+
=m
m
A c
α
σ (4-13)
98
Eq. (4-13) is the constitutive equation which describes the behaviour of pulp suspension
at shear stresses above the critical shear stress (σc~278 Pa). The constants of this model
were found to be α=0.295 and m=7.95 for the 6 wt.% SGW pulp fibre suspensions
examined here.
Figure 4-11: Master curve obtained from steady-state velocity profiles of Figure 4-10.
Solid line is the fit of Eq. (4-11) to the data with α=0.295 and m=7.95.
4.4. Summary
Rheological experiments with concentrated pulp suspensions showed that they
exhibit many of the hallmarks of glassy colloids and pasty materials, namely strong
dependence of rheology on the rest time, thixotropy and yielding. Their thixotropic
response was marked by a fast characteristic time in response to sudden changes of shear
stress. In contrast to the structure breakdown, kinetics of structure build-up found to be
dependant on the previous shear history. The transient response of pulp to step changes in
the stress level was described adequately by KWW functions from which single
characteristic times for build-up and breakdown processes were obtained.
99
The flow curves of these dense pulp suspensions were found to exhibit a plateau
where a slight change of the applied shear stress led to a dramatic change in the
corresponding shear rates. The direct implication of such a plateau in practice is that there
is no stable flow below a critical shear stress due to viscosity bifurcation. This in turn
results in a discontinuity in the slope of the velocity profiles in the vicinity of the yielding
radius where the Herschel-Bulkley model fails to predict the flow. This study
demonstrates that pulp viscosity and the critical shear stress increase with the time of rest,
while the discontinuity in the velocity profiles becomes more pronounced.
The velocity profiles obtained for pulp suspensions at different vane rotational
speeds were found to fall along a single master curve. This master curve was then used to
propose a constitutive rheological model to describe the flow behaviour of pulp at shear
stresses above the critical shear stress.
In summary, this study shows that dense pulp fibre suspensions beyond a critical
fibre concentration taking into account the fibre size and flexibility are thixotropic
yielding materials and are prone to exhibit shear-banding. The discontinuous change in
the slope of the velocity profiles in the vicinity of the yielding radius suggests either
shear-banding or slippage of fibre flocs over each other. These must be distinguished in
the future in order to obtain a clear picture and develop design criteria for the processing
of these systems.
100
5. Conclusions, Contributions to the Knowledge and
Recommendations
5.1. Conclusions
The rheology of commercial pulp fibre suspensions was studied at fibre mass
concentrations of 0.5-6 wt.% using conventional rheometry and coupled UDV-rheometry
technique. Conventional rheometry was found to fail when used to study the rheology of
pulp fibre suspensions at low shear rates due to the presence of wall slip. On the other
hand, the coupled UDV-rheometry technique has shown good suitability for the task,
since it allowed the measurement of local velocities within the gap of the rheometer
regardless of any existing wall artefacts.
The coupled UDV-rheometry technique was used to measure the apparent yield
stress of pulp fibre suspensions through the measurement of the steady-state velocity
profiles across the gap of the rheometer. The apparent yield stress values obtained by this
technique were in good agreement with those obtained by applying linear shear stress
ramps using a stress-controlled rheometer. However, these measurements resulted in
significantly different values compared with those obtained from a rate-controlled
rheometer by applying constant shear rates. The results obtained by the three
measurement techniques examined in this study were compared, and models were
proposed to predict the apparent yield stress as a function of fibre mass concentration. It
was shown that the coupled UDV-rheometry technique is most reliable to measure
apparent yield stress values to be used in designing mixing operations due to geometrical
similarities and the measurement of the velocities within the yielded region of the
rheometer. The measurement technique developed in this study can be used not only for
pulp fibre suspensions, but also for any visco-plastic material exhibiting complex
rheological behaviour.
Conventional rheometry and coupled UDV-rheometry were further used to study
the post-yield flow behaviour of pulp fibre suspensions. Pulp fibre suspensions were
found to be shear-thinning materials up to a critical shear stress, after which Newtonian
behaviour prevailed. The velocity profiles were fitted with a Herschel-Bulkley model to
101
obtain the model parameters. These parameters were then used to describe the flow
curves obtained by conventional rheometry. Herschel-Bulkley model was found to
adequately describe the flow behaviour up to the critical shear stress required to
commence the Newtonian regime. However, a discrepancy was found between the model
predictions and the flow curves obtained by the conventional rheometry at low shear
rates. Further analysis of the velocity profiles proved the presence of wall slip at low
shear rates, which was found to be the reason for the discrepancy observed in the results.
The UDV-rheometry technique was also used to study the effect of important
process parameters such as pH and lignin content on the rheology of pulp fibre
suspensions. Increasing pH over the alkaline region increased the viscosity and apparent
yield stress of pulp fibre suspensions as the fibre volume fraction increased due to fibre
swelling. The effect of pH on the rheology was less significant as the lignin content was
increased in the TMP fibre suspensions. Lignin serves as a glue to keep fibres together
and prevent them from swelling. This study showed that conventional rheometry fails at
low shear rates when used to study complex pulp fibre suspensions. Additionally,
velocimetry techniques such as UDV are useful to explore and correct the effects of
experimental perturbations such as wall slip.
The velocity profiles measured for pulp fibre suspensions exhibited a progressive
decrease in transition from yielded to un-yielded region up to a certain fibre mass
concentration. At higher concentrations the velocity profiles exhibited an abrupt change
in the slope in transition to the un-yielded region, implying the presence of shear banding.
Therefore to study this phenomena and effects such as thixotropy in more detail pulp
fibre suspensions at 6 wt.% were studied by means of conventional rheometry and
coupled UDV-rheometry techniques. Pulp suspensions were found to exhibit thixotropy
based on the measurements of the hysteresis loops and step changes in the applied shear
stress. Structure break-down and build-up were studied by means of appropriate
experimental protocols, and characteristic time scales of the process were obtained by
means of a stretched exponential function. It was shown that structure break-down and
build-up in pulp suspensions are basically governed by the shear-induced collisions.
102
The flow curves obtained for 6 wt.% pulp fibre suspensions exhibited a plateau
over which no measurements could be made. This plateau was found to correspond to the
viscosity bifurcation effect, implying the presence of instability below a critical shear
rate. The direct implication of such a plateau was found to be an abrupt change in the
slope of the velocity profiles in transition to the un-yielded region within the gap of the
rheometer. The Herschel-Bulkley model failed to describe the velocity profiles. To
propose a constitutive rheological model to describe the flow behaviour of the
concentrated pulp suspensions in the sheared region of the rheometer, the velocity
profiles obtained at different vane rotational rates were used to construct a master curve.
This master curve was then used to propose a constitutive model for pulps which cannot
be modeled as ideal yield stress fluids. This study shows that pulp fibre suspensions
exhibit a change in rheological behaviour as the fibre mass concentration, increases
beyond a critical concentration taking into account the fibre size and flexibility.
5.2. Contributions to the Knowledge
The contributions to knowledge that have been resulted from this research work
are identified as follows:
1. Conventional rheometry fails to study the rheology of pulp fibre suspensions
at low shear rates due to the presence of wall slip. However, conventional
rheometers can be efficiently modified with velocimetry techniques such as
ultrasonic Doppler velocimetry to become powerful tools to study complex
systems such as pulp fibre suspensions. The main advantage of the latter is the
measurement of the actual velocity profiles across the gap of the rheometer
regardless of the presence of any wall artefacts.
2. Based on the above mentioned coupled UDV-rheometry technique the
apparent yield stress of pulp fibre suspensions was measured using the radius
of shearing and the torque distribution in the gap of the rheometer. This
method of measuring the apparent yield stress is the most reliable when used
with complex suspensions such as pulp fibre suspensions to provide raw data
for mixing operation applications. This velocimetry-based apparent yield
103
stress measurement technique can be used in suspensions with complex
rheological behaviour, particularly those with large particles.
3. The thixotropy and shear banding effects in concentrated pulp fibre
suspensions were studied for the first time in the literature. It is reported that
pulp fibre suspensions at high fibre mass concentrations are thixotropic
materials exhibiting shear banding instability. It was found that constitutive
rheological models such as Herschel-Bulkley are not adequate to describe the
rheology of concentrated pulp fibre suspensions.
4. The transient response of pulp to step changes in the stress was studied. In
contrast to the structure breakdown, kinetics of structure build-up was found
to be dependant on the previous shear history. The transient behaviour was
described by KWW functions from which single characteristic times for both
build-up and breakdown were obtained. This is the first time that the kinetics
of structure break-down and build-up is studied in the literature for pulp fibre
suspensions.
5.3. Recommendations for Future Work
Several important aspects of pulp fibre suspension rheology are yet to be studied.
These are recommended below for possible future work.
1. This study reports that different apparent yield stress measurement techniques and
definitions may result in different values. It is worthwhile to study the apparent
yield stress both in macroscopic and microscopic scales. At macroscopic scale
apparent yield stress can be measured by means of conventional rheometry and/or
coupled velocimetry-rheometry techniques, while at a microscopic scale it can be
measured by techniques such as light scattering echo. This will shed insight into
the yielding transition and may clarify the existing ambiguity.
2. The apparent yield stress measurement technique developed in this study by
means of coupled velocimetry-rheometry technique should be further established
104
by measuring the apparent yield stress of different systems other than pulp
suspensions including ideal yield stress fluids and those which exhibit shear
banding.
3. Pulp fibre suspensions were found to exhibit wall slip at low shear rates.
However, the governing microscopic mechanisms are not well-known. Although
of limited practical significance, it is worthwhile to study and further examine the
phenomena of wall slip in these systems at low shear rates.
4. Pulp fibre suspensions were found to exhibit a change in the rheological
behaviour from an ideal yield stress fluid to a suspension with shear banding as
the fibre mass concentration increases. However, the exact mechanisms for such
a change in behaviour are not yet known. Factors such as fibre flexibility, length
and size distribution that may play a role in these phenomena should be examined
in more detail in the future.
5. Concentrated pulp fibre suspensions were found to exhibit thixotropy and shear
banding instability. These should be modeled by means of constitutive models
which include a structure parameter which evolves with time and depends on the
flow kinematics.
105
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Appendix
Appendix A: Ultrasonic Doppler Velocimetry
In this appendix the principles of ultrasonic Doppler velocimetry, its advantages
as well as limitations are reviewed. More information can be found in the user manual of
the instrument (DOP2000, Signal Processing, Switzerland). Ultrasonic Doppler
velocimetry was developed over 30 years ago as a diagnostic medical imaging. Over the
years, this technique has found its applications to important area of fluid dynamics, for
example, in areas such as product mixing, fluid transportation etc. Ultrasonic Doppler
velocimetry can be performed in two modes of continuous and pulsed velocimetry. Here,
we shall focus on the pulsed ultrasonic Doppler velocimetry since a pulsed ultrasound
Doppler velocimeter has been used in this study.
Principles of Pulsed Ultrasound Doppler Velocimetry
In a pulsed ultrasound Doppler velocimeter (UDV), an emitter periodically sends
ultrasound beams to a fluid and a receiver collects the reflected pulses by the moving
particles that may be present in the path of the ultrasound beam. Often, the same
transducer is used as both an emitter and a receiver. Figure A-1 shows a picture of the
ultrasound Doppler velocimeter coupled with a rate-controlled rheometer used in this
study.
A pulsed ultrasound Doppler velocimeter measures the velocity and the depth of
the particles within a moving fluid by measuring two parameters. First, it measures the
frequency of the emitted and reflected pulses resulted from motion of the particles. In
addition, it measures the time required for an ultrasound beam to travel from the emitter
to the particle and reflect back to the receiver. This parameter is referred to as the time
delay. By measuring these two parameters, the depth of the moving particle can be
measured by Eq. (A-1):
2
. fTcy = (A-1)
125
where c is the velocity of sound in the medium and Tf is the time delay between an
emitted burst and the echo reflected by the particle.
Figure A-1: Ultrasound Doppler velocimeter coupled with a rate controlled rheometer.
The same transducer is used as an emitter and a receiver.
By having the time interval between two subsequent ultrasound bursts, Tprf , and
the angle at which the particle is moving in relation to the axis of the ultrasound beam, θ,
the change in depth of the particle can be measured by Eq. (A-2):
)(2
cos)( 1212 TTc
Tyy prf −×=××=− θν (A-2)
The time difference, T2-T1, is a function of the phase shift of the received echo, δ, and can
be measured by Eq. (A-3):
0
122 f
TT×
=−π
δ (A-3)
where f0 is the ultrasound emitting frequency. The particle velocity can then be calculated
by Eq. (A-4):
126
θθπ
δ
cos2cos4 00 ××
×=
×××
×=
f
fc
Tf
cv d
prf
(A-4)
Therefore, the depth and the velocity of a moving particle can be measured in a fluid and
in the direction of the ultrasound beam.
Advantages and Limitations
UDV is a non-intrusive technique which can be used to measure the velocity
distribution within a moving fluid. Its main advantage is that it can be easily used with
both transparent and opaque fluids, in contrast to the most of the other velocity
measurement techniques. However, there are a number of limitations/assumptions in
making use of such a technique. The main limitation is that there is a maximum velocity
that can be measured for each pulse repetition frequency (PRF). This maximum velocity
can be measured according to Eq. (A-5):
prfTf
cu
×××=
θcos4 0
max (A-5)
If a velocity higher than this maximum is measured, a phenomenon referred to as aliasing
occurs which affects the accuracy of the measured data. This means that all frequencies
above the half of the sampling frequency are folded back in the low frequency region.
Similarly, there is a limitation in the measurement of the maximum depth. The
maximum measurable depth can be calculated by Eq. (A-6):
2max
cTy
prf ×= (A-6)
From Eqs. (A-5) and (A-6) it is evident that reducing PRF or increasing Tprf will increase
the measureable depth but decreases the maximum measurable velocity. This can be more
clearly shown by Eq. (A-7):
ef
cuy
8
2
maxmax = (A-7)
In other words, there is a maximum measurable depth corresponding to a maximum
measureable velocity, this can often impose a limitation in the practical situations.
127
In addition to the above limitations, it is presumed that the ultrasound beam only
travels in a straight line with a constant rate of attenuation. The speed of sound in the
medium is assumed to be constant and the ultrasound beam is assumed to be infinitely
thin with all echoes originating from its central axis. Obviously, these are not satisfied in
all situations.
Resolution
Resolution is the ability of the instrument to distinguish two objects adjacent to
each other in the fluid and is divided into spatial and temporal resolution. Spatial
resolution in turn can be divided into axial and lateral resolution. Axial resolution is the
ability of the instrument to identify objects in the direction of the ultrasound beam while
lateral resolution is the ability to identify two objects perpendicular to the beam’s
direction. These resolutions have to be adjusted properly in order to be able to capture the
true flow field of the fluid within the system.
The lateral resolution can be increased by decreasing the width of the ultrasound
beam. The beam’s width can be decreased by using a higher frequency transducer,
focusing the beam or by decreasing the gain. The axial resolution on the other hand can
be improved by using higher frequency transducers at the expense of decreasing the
penetration. Therefore, higher frequencies are used to capture the structures close to the
transducer. In this study the spatial resolution was set between 0.19–0.25 mm, with a
temporal resolution of 45–55 ms/profile and velocity resolution of 0.025 mm/s.